Inadequately controlled hypertension (systolic blood pressure of > 150 mmHg or diastolic pressure > 100 mmHg on anti-hypertensive medications) Uncontrolled blood pressure and hypertension: systolic blood pressure (SBP) > 140 mm Hg or diastolic blood pressure (DBP) > 90 mm Hg within 14 days prior to registration; patients are permitted to be receiving multiple anti-hypertensive medications (unless otherwise indicated in the study); all blood pressure measurements within the 14 days prior to registration and on day 1 of cycle 1 must be SBP =< 140 and DBP =< 90; an exception can be made by a healthcare provider for a patient with a single blood pressure elevation who upon rechecking has a normal blood pressure Hypertension:* Patients, 3-17 years of age must have a blood pressure that is =< 95th percentile for age, height and gender at the time of registration** The normal blood pressure by height, age and gender tables can be accessed in the Generic Forms section of the Pediatric Brain Tumor Consortium (PBTC) members� webpage* Patients who are >= 18 years of age must have a blood pressure that is < 140/90 mm of Hg at the time of registration* Note: if a blood pressure (BP) reading prior to registration is above the 95th percentile for age, height and gender it must be rechecked and documented to be =< the 95th percentile for age, height and gender prior to patient registration Patients must not have uncontrolled hypertension (defined as systolic blood pressure > 140 mm Hg and/or diastolic blood pressure > 90 mm Hg which cannot be controlled by anti-hypertensive therapy) Adult patients with hypertension not controlled by medical therapy (hypertension defined as systolic blood pressure > 150 mmHg or diastolic pressure > 90 mmHg despite optimal medical management); pediatric patients must have blood pressure (BP) within normal limits (WNL) for age; NOTE: blood pressure within the upper limit of normal is defined as: blood pressure =< the 95th percentile for age, height, and gender, and not be receiving medication for treatment of hypertension Adequate blood pressure defined as:* A blood pressure (BP) =< the 95th percentile for age, height, and gender measured; adequate blood pressure can be achieved using medication for treatment of hypertension Patients not achieving adequate blood pressure in spite of antihypertensive therapy for control of blood pressure Inability to home monitor blood pressure Inadequately controlled hypertension (systolic blood pressure of > 150 mmHg or diastolic pressure > 90 mmHg on anti-hypertensive medications) History of uncontrolled hypertension, defined as blood pressure > 150/95 mmHg, or systolic blood pressure > 180 mmHg when diastolic blood pressure < 90 mmHg, on at least 2 repeated determinations on separate days within 3 months prior to study enrollment Significant active cardiovascular or pulmonary disease at the time of study entry, including:* Uncontrolled high blood pressure (i.e., systolic blood pressure > 150 mm Hg, diastolic blood pressure > 95 mm Hg)* Pulmonary hypertension* Uncontrolled asthma or oxygen (O2) saturation < 90% by pulse oximetry on room air* Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement* Medically significant (symptomatic) bradycardia* History of arrhythmia requiring an implantable cardiac defibrillator Uncontrolled high blood pressure (i.e., systolic blood pressure >= 160 mmHg, diastolic blood pressure >= 90 mmHg) Patients with uncontrolled hypertension are ineligible; uncontrolled hypertension is defined as follows:* Patients aged =< 17 years: greater than 95th percentile systolic and diastolic blood pressure based on age and height which is not controlled by one anti-hypertensive medication* Patients aged > 17 years: systolic blood pressure >= 140 mmHg and/or diastolic blood pressure >= 90 mmHg that is not controlled by one anti-hypertensive medication Participants with uncontrolled sustained hypertension which will be defined as systolic blood pressure > 140, and diastolic blood pressure > 90, even with use of anti-hypertensive medications Significant active cardiovascular or pulmonary disease at the time of study entry, including* Uncontrolled high blood pressure (i.e., systolic blood pressure > 180 mm Hg, diastolic blood pressure > 95 mm Hg) * Pulmonary hypertension * Uncontrolled asthma or oxygen (O2) saturation < 90% by ABG (arterial blood gas) analysis or pulse oximetry on room air * Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement * Medically significant (symptomatic) bradycardia Uncontrolled hypertension (despite medical therapy); blood pressure should be < 140/90 in accordance with American Heart Association definition of hypertension Patients must be willing and able to check and record daily blood pressure readings; blood pressure cuffs will be provided to patients randomized to Arm III Patients who are receiving anti-hypertensive medications for control of blood pressure at the time of enrollment are not eligible for this trial No uncontrolled hypertension (systolic blood pressure =< 160 millimeters of mercury [mmHg] or diastolic =< 100 mmHg); patients with hypertension must be adequately controlled with appropriate anti-hypertensive therapy or diet Patients must not have inadequately controlled hypertension; patients must have documented blood pressures of systolic blood pressure (SBP) < 150 and diastolic blood pressure (DBP) < 90 within 14 days of starting randomization; blood pressure medications (any number) are permitted Low resting systolic blood pressure: < 90 mmHg Use of any other blood pressure lowering medication for treatment of hypertension within 30 days of enrollment except calcium channel blockers and diuretics Patients with hypertension on medical management must have systolic blood pressure < 150 mmHG or diastolic pressure < 90 mmHG at study entry Patients must be willing and able to check and record daily blood pressure readings when randomized to cediranib containing arm Patients with known significant active cardiovascular or pulmonary disease at the time of study entry are INELIGIBLE including:* Uncontrolled hypertension (i.e., systolic blood pressure >180 mm Hg, diastolic blood pressure > 95 mm Hg); use of anti-hypertensive agents to control hypertension before cycle1 day 1 is allowed* Pulmonary hypertension* Uncontrolled asthma or oxygen (O2) saturation < 90% by arterial blood gas analysis or pulse oximetry on room air* QT syndrome, or torsades de pointes* Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement* Medically significant (symptomatic) bradycardia* History of arrhythmia requiring an implantable cardiac defibrillator* Baseline prolongation of the rate-corrected QT interval (QTc) (e.g., repeated demonstration of QTc interval > 480 milliseconds, or history of congenital long Patients must be willing and able to check and record daily blood pressure readings if receiving cediranib Patients with clinically significant cardiovascular disease are excluded* Inadequately controlled hypertension (HTN) (systolic blood pressure [SBP] >= 160 mmHg and/or diastolic blood pressure [DBP] >= 90 mmHg despite antihypertensive medication)* History of cerebrovascular accident (CVA) within 6 months* Myocardial infarction or unstable angina within 6 months* New York Heart Association class II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia* Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)* Clinically significant peripheral vascular disease Patients with clinically significant cardiovascular disease are excluded* Inadequately controlled hypertension (HTN) (systolic blood pressure [SBP] > 160 mmHg and/or diastolic blood pressure [DBP] > 90 mmHg despite antihypertensive medication)* History of cerebrovascular accident (CVA) within 6 months (see additional requirement for adjuvant protocols)* Myocardial infarction or unstable angina within 6 months (see additional requirement for adjuvant protocols)* New York Heart Association grade II or greater congestive heart failure * Serious and inadequately controlled cardiac arrhythmia* Significant vascular disease (e.g. aortic aneurysm, history of aortic dissection)* Clinically significant peripheral vascular disease