Non-pregnant and non-lactating Participants who are pregnant or lactating Is pregnant or lactating Pregnant or lactating Not pregnant or lactating, willing to prevent pregnancy while on study and for 6 months after the last dose of XMT-1522 Currently pregnant or lactating Subject is pregnant or lactating Lactating or pregnant woman Patient is pregnant or lactating. Pregnant or lactating Subject who is pregnant or lactating. Not pregnant or lactating Lactating woman Pregnant or lactating EXCLUSION - TREATMENT: Pregnant or lactating EXCLUSION - INFUSION: Pregnant or lactating Lactating or pregnant TREATMENT EXCLUSION: Pregnant or lactating Lactating or pregnant Patient is pregnant or lactating The patient is pregnant or lactating. Pregnant or lactating Pregnant or lactating Pregnant or lactating Pregnant or lactating. Pregnant or lactating Pregnant or lactating Pregnant or lactating EXCLUSION - TREATMENT: Pregnant or lactating If they are pregnant or lactating Pregnant or lactating, or intending to become pregnant during the study Pregnant or lactating, or intending to become pregnant during the study Non-pregnant and non-lactating Pregnant or lactating, or intending to become pregnant during or within 5 months after the last dose of study treatment Exclusion Criteria Related to Atezolizumab: Pregnant, lactating, or not using adequate contraception. Subjects who are pregnant or are lactating Currently pregnant, lactating or breastfeeding. Pregnancy and/or lactating. Pregnant or lactating Lactating or pregnant Is pregnant or lactating DONOR: Pregnant or lactating Pregnant or lactating, or intending to become pregnant during the study Lactating or pregnant Pregnant or lactating Pregnant or lactating individuals. Lactating or pregnant Pregnant or lactating subjects Be pregnant or lactating PRIOR TO LYMPHODEPLETION: Pregnant or lactating Pregnant or lactating individuals. Subjects must not be pregnant or lactating Pregnant or lactating Pregnant or lactating Subject that is pregnancy or lactating Pregnant or lactating woman AT THE TIME OF INFUSION: Pregnant or lactating Pregnant or lactating Pregnant or lactating individuals. Pregnant or lactating Pregnant or lactating RECIPIENT: Pregnant or lactating Pregnant or lactating Pregnant or lactating. Pregnant or lactating Lactating or pregnant Pregnant or lactating Pregnant or lactating Pregnant or lactating pregnant or lactating Pregnant or Lactating. Pregnant or lactating Pregnant, lactating, or not using adequate contraception Pregnant, lactating or not using adequate contraception. Lactating or pregnant Is pregnant or lactating. Subjects who are pregnant or lactating; Non-pregnant and non-lactating. If they are pregnant or lactating Who are pregnant and/or lactating Pregnant or lactating Pregnant or lactating Pregnant or lactating, or intending to become pregnant during the study Subject is pregnant or is lactating Subject is pregnant or lactating Pregnant or lactating, or intending to become pregnant during the study Subject is pregnant or lactating Pregnant or lactating Pregnant or lactating Participant is pregnant or lactating. The participant is pregnant prior to randomization or lactating. Subject is pregnant or lactating Pregnant or lactating Pregnant or lactating or intending to become pregnant during the study Participants who are pregnant or lactating Lactating or pregnant subjects Lactating or pregnant Pregnant or lactating. Lactating or pregnant Not pregnant or lactating Are pregnant or lactating. Pregnant or lactating Participant is pregnant or lactating Participants who are pregnant or lactating Pregnant or lactating Lactating or pregnant subjects Currently pregnant or lactating AT THE TIME OF INFUSION: Pregnant or lactating Lactating or pregnant. Subjects who are pregnant or lactating. Pregnancy and/or lactating A pregnant or lactating woman. Pregnant or lactating. Patient is pregnant or lactating Pregnant or lactating Pregnant or lactating Lactating or pregnant Pregnant or lactating Pregnant or lactating Lactating or pregnant. Pregnant or lactating Pregnant or lactating pts DONOR: not pregnant or lactating Pregnant or lactating Pregnant or lactating Pregnant or lactating DONOR: Not pregnant or lactating Pregnant or lactating subjects. Woman who is pregnant or lactating Participant is pregnant or lactating Pregnant or lactating Subject is pregnant or lactating. Are pregnant or lactating Patient is pregnant or lactating The participant is pregnant or lactating. Pregnant or lactating Currently lactating. Pregnant or lactating The participant is pregnant or lactating Self-report of being pregnant or lactating Subject is pregnant or lactating Pregnant or lactating Lactating or pregnant Lactating or pregnant Pregnant or lactating The patient is pregnant or lactating The subject is known or suspected to be pregnant or lactating Pregnant or lactating Pregnant and/or lactating within 1 year prior to screening breast MRI Must be non-pregnant and non-lactating for at least one year prior to pre-registration Pregnant or lactating Lactating Subjects who are pregnant and/or lactating are not eligible Not pregnant or lactating and does not intend to become pregnant during the study Pregnant or lactating The patient is pregnant or lactating Subjects who are pregnant or lactating or who suspect they might be pregnant Subjects who are pregnant or lactating or who suspect they might be pregnant Subjects who are pregnant or lactating or who suspect they might be pregnant Patient who is pregnant and/or lactating Subject is pregnant or lactating Non-pregnant and non-lactating Not pregnant or not lactating Participants who are pregnant, lactating, or who suspect they might be pregnant are not eligible Pregnant or lactating Subjects who are pregnant or lactating Subjects who are pregnant or lactating or who suspect they might be pregnant The subject is pregnant or lactating. Subject is pregnant or lactating The patient is pregnant or lactating. Pregnant or lactating, or intending to become pregnant during the study Patient is pregnant or breastfeeding Patient is pregnant or breastfeeding Patient must not be pregnant or breastfeeding Patient is pregnant or lactating and does not agree to stop breastfeeding. Patient is pregnant or breastfeeding The patient is pregnant or is breastfeeding. Patient is pregnant or breastfeeding Patient must not be pregnant or breastfeeding Patient must not be pregnant and/or breastfeeding Patient is pregnant or breastfeeding Patient is breastfeeding. The patient is pregnant or breastfeeding Patient is pregnant, lactating, or breastfeeding Patient must not be pregnant and/or breastfeeding Patient is pregnant or breastfeeding Patient is pregnant or breastfeeding Patient must not be pregnant and/or breastfeeding Patient must not be pregnant and/or breastfeeding Patient is pregnant or lactating and does not agree to stop breastfeeding. Patient must NOT be breastfeeding. Patient who is pregnant and/or breastfeeding Patient is lactating (breastfeeding) or pregnant Patient must not be pregnant or breastfeeding Patient must not be pregnant or breastfeeding Patient must not be pregnant or breastfeeding Patient is pregnant or breastfeeding Patient must not be pregnant or breastfeeding Female patients who are pregnant and/or lactating are not eligible Female subjects who are both lactating and breastfeeding Female subjects who are pregnant or lactating. Pregnant or lactating female Female patients who are lactating or pregnant Is a pregnant or lactating female Female subject who is lactating/breastfeeding. Pregnant or lactating female. Pregnant or lactating female Pregnant or lactating female If female, the patient is pregnant or lactating. Female only: pregnant or lactating Lactating female Female patients who are pregnant or lactating Pregnant or lactating female Female subject who is lactating or pregnant Female subject is pregnant or lactating Pregnant or lactating female Female patients who are pregnant or lactating Pregnant or lactating female. Pregnant or lactating female Pregnant or lactating female Pregnant or lactating female Pregnant or lactating female Female patients who are pregnant or lactating are not eligible to receive treatment but can be followed for natural history Female subject who is pregnant or lactating. Is a pregnant or lactating female. Pregnant or lactating female. Pregnant or lactating female. The recipient is pregnant or a lactating female DONOR: Lactating female Lactating or pregnant female. Pregnant or lactating female patients. Is a pregnant or lactating female. Female subject who is pregnant or lactating Male or non-pregnant, non-lactating female Pregnant or lactating female Female patients who are pregnant or lactating. Male or non-pregnant and non-lactating female Lactating female. Is a pregnant or lactating female Female: pregnant or lactating Female patients who are lactating, breastfeeding, or pregnant Pregnant or lactating female Lactating female Female patients who are pregnant or lactating Female patients who are lactating or pregnant The patient, if female, is pregnant or lactating Pregnant or lactating female If female, is lactating. Pregnant or lactating female Lactating female or female who becomes pregnant prior to transition to this study. If female, neither pregnant nor lactating. Female patients who are pregnant or lactating Male or non-pregnant, non-lactating female patients Pregnant or lactating female. Pregnant or lactating female EXPANSION COHORT ONLY: Female subjects who are pregnant or lactating are not eligible to participate in this study Pregnant or lactating female; Lactating female Female subject is pregnant or lactating If female, participant is pregnant or lactating at the time of enrollment, or has plans to become pregnant during the study Is a pregnant or lactating female. Pregnant or lactating female Pregnant or lactating female. Pregnant or lactating female. Pregnant or lactating female Female subjects who are pregnant or lactating at Screening, or plan to become pregnant while on study or within 6 months after the last dose of study drug Pregnant or lactating female. Is a pregnant or lactating female Female patients who are pregnant or lactating Pregnant or lactating female Female patients who are lactating or pregnant Female patients who are pregnant or lactating and breastfeeding Lactating female Pregnant or lactating female or female of child-bearing potential not employing adequate contraception. Female subjects who are pregnant or lactating Lactating or pregnant female. Female patients who are pregnant or lactating. Subject is a lactating or pregnant female. Female patients who are lactating or pregnant If female, pregnant or lactating Pregnant or lactating female Pregnant or lactating female. For female patients: the patient is pregnant or lactating. Is a pregnant or lactating female. Any patients with allergy to the drug; and any pregnant female or lactating. For female patients: the patient is pregnant or lactating. Female subjects of childbearing potential must not be pregnant or lactating at screening Female subjects that are pregnant or lactating. Female patients who are pregnant or lactating at the baseline/screening visit Lactating female patient. Female patients who are lactating or pregnant Pregnant or lactating female. Pregnant or lactating female patients Female patients who are lactating or pregnant Female patients who are lactating or pregnant Pregnant or lactating female. Female participants of childbearing age must not be lactating Pregnancy or lactating female Pregnant or lactating female Female subjects who are pregnant or lactating Pregnant or lactating female Female who is lactating/breastfeeding. Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in 03-C-0277 Subject’s must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled on protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Enrolled in another treatment protocol Subjects must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled in protocol 03-C-0277 Subject must be co-enrolled in protocol 03-C-0277 Subjects must be co-enrolled on protocol 03-C-0277 Male or female subjects of the age defined in the original protocol they were enrolled. Subjects will not be treated with any radiation, chemotherapy, or investigational agents while enrolled in this protocol. Participants enrolled in a radiation de-intensification protocol Previously enrolled patients who completed this protocol FOR THE 31 SUBJECTS ENROLLED IN YEAR 1: Pregnant female Subjects may be enrolled at any point in diagnosis or treatment Subject enrolled into the protocol BDS-USHPV and identified as eligible for the longitudinal protocol • Subjects enrolled into protocol BDS-USHPV with a baseline colposcopy and biopsy procedure and not treated. Patient must be enrolled or being considered for enrollment on protocol 2010-0085 Is a female subject who is pregnant or breastfeeding. Subject is pregnant or breastfeeding. Female subject who is pregnant or breastfeeding. If female, subject is pregnant and/or breastfeeding. HEALTHY SUBJECT: Not pregnant or breastfeeding Subject is pregnant or breastfeeding. The subject is pregnant or breastfeeding The subject is pregnant or breastfeeding The subject is pregnant or breastfeeding Female subject who is pregnant or breastfeeding The subject is pregnant or breastfeeding. Subject is pregnant or breastfeeding or intends to get pregnant within 28 days of enrolling into the study. Subject if female, is pregnant or breastfeeding The subject is pregnant or breastfeeding Subject is pregnant or breastfeeding The subject is pregnant or breastfeeding. Is the subject breastfeeding? The subject is pregnant or breastfeeding The subject is pregnant or breastfeeding The subject is pregnant or breastfeeding Subject is pregnant or breastfeeding. The subject is pregnant Pregnant or lactating patients Patients who are pregnant or lactating will not be eligible; pregnant patients are ineligible Patients who are pregnant or lactating Pregnant or lactating patients Patients must not be pregnant or lactating Patients who are pregnant or lactating. Patients who are pregnant, lactating, or breastfeeding Patients who are pregnant or lactating Pregnant or lactating patients Pregnant or lactating patients Patients may not be pregnant or lactating at study registration Patients who are pregnant or lactating. Patients must not be pregnant of lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Pregnant or lactating patients Patients who are pregnant or lactating Pregnant or lactating patients Pregnant or lactating patients Patients who are pregnant or lactating. Patients in pregnant or lactating Patients who are pregnant or lactating are NOT eligible for participation Patients who are pregnant and/or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating; Patients who are pregnant or lactating Patients who are pregnant and/or lactating are NOT eligible for participation Pregnant or lactating patients Pregnant or lactating patients Pregnant or lactating patients Pregnant or lactating patients Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Pregnant or lactating patients Pregnant or lactating patients Pregnant or lactating patients Patients cannot be lactating Patients who are pregnant or lactating Pregnant or lactating patients Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating or not practicing adequate contraception Patients who are pregnant or lactating are not eligible Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating Patients who are pregnant or lactating No patients known to be pregnant or lactating Patients pregnant or lactating Patients who are pregnant or lactating Patients who are or might be pregnant or lactating Pregnant or lactating patients Pregnant or lactating patients Patients who are pregnant or lactating Patients who are pregnant or lactating Female subjects: Female subjects must be either: Female subjects must be either: Female participants must either: Female patients who: Female subjects must be: Female participants who: Female participants who: Female patients must either: Female Female participants who: Must be female. Female Female Female participants must not be breastfeeding Female participants who: Female participants who: Female participants who: Female >=18 years Female participants who: Female participants who: Female participants who: Female participants who: Female participants who: Female participants Female participants who: Female participants who: Female participants who: Female participants will be excluded from the trial if they become pregnant; female participants can use whichever method of contraception that they prefer Be female. Female Patient: Female Female Female participants who: Female patients who are pregnant are ineligible Pregnant female patients are not eligible for this study Female patients who are pregnant are ineligible Pregnant female patients; breastfeeding female patients; male patients with partners currently pregnant. Pregnant or breastfeeding female patients Female subjects of childbearing potential must not be pregnant or breastfeeding Pregnant or breastfeeding female. Female patients may not be pregnant or breastfeeding Female patients who are pregnant or breastfeeding Female patients who are pregnant (positive beta-HCG) or breastfeeding. Female participants who are pregnant or breastfeeding are excluded. Pregnant or breastfeeding female patients Female patients who are pregnant or breastfeeding A female participant is eligible to participate if she is not pregnant , not breastfeeding, and at least one of the following conditions applies: Pregnant or breastfeeding (female only) Female subjects who are breastfeeding, pregnant, or plan to become pregnant during the study or within 3 months following the last dose of investigational product Female subjects who are pregnant or breastfeeding Female patients who are pregnant or breastfeeding Pregnant or breastfeeding female Participant is pregnant or is a breastfeeding female Female patients who are breastfeeding. Pregnant or breastfeeding female patients. Female only: pregnant or breastfeeding Are female and pregnant or breastfeeding. Pregnant or breastfeeding female. Female patient who is breastfeeding. Female patients who are pregnant are ineligible Female patients who are pregnant are ineligible Female patients who are pregnant are ineligible Female patients who are pregnant or breastfeeding Female patient who is pregnant or breastfeeding Female patients who are pregnant are not eligible for this study Is a female who is pregnant, nursing, or breastfeeding, or who intends to become pregnant during the participation in the study Is a female who is pregnant, nursing, or breastfeeding, or who intends to become pregnant during the participation in the study Pregnant or breastfeeding woman or female who intends to become pregnant during the participation in the study. Pregnant female Female patients who are pregnant or breastfeeding Female patients who are pregnant are ineligible A female subjects is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: Female subjects that are pregnant or breastfeeding are not eligible Pregnant, lactating or actively breastfeeding female subjects Female patients who are pregnant are not eligible Female patients who are pregnant or currently breastfeeding Female patients who are breastfeeding or pregnant Female patients who are pregnant or breastfeeding Female subjects that are pregnant or breastfeeding. Female patients who are pregnant are ineligible (Female only) not breastfeeding (Female only) is not breastfeeding DONOR: (Female only) is not breastfeeding Female patient is pregnant, breastfeeding, or premenopausal and not using an effective method of contraception Female subjects who are pregnant or breastfeeding. Any female that is trying to get pregnant Female subjects who are pregnant or breastfeeding. Female patients who are pregnant or breastfeeding Female subjects who are pregnant or breastfeeding Female subjects who are pregnant or breastfeeding Female who is pregnant or breastfeeding Non-pregnant female volunteer Pregnant female Pregnant female Female patients who are pregnant or breastfeeding Female patients who are pregnant or actively breastfeeding