Cediranib Maleate and Cilengitide in Treating Patients With Progressive or Recurrent Glioblastoma

Inclusion Criteria: * Patients must have histologically proven glioblastoma which is progressive or recurrent following radiation therapy and/or chemotherapy; patients with previous low grade glioma who progressed after radiotherapy and/or chemotherapy and are biopsied and found to have glioblastoma are eligible * Patients must have measurable contrast-enhancing progressive or recurrent glioblastoma by magnetic resonance imaging (MRI) imaging within two weeks of starting treatment; patient must be able to tolerate MRIs; computed tomography (CT) scans cannot be substituted for MRIs in this study * Patients must have recovered from severe toxicity of prior therapy; an interval of at least 3 months must have elapsed since the completion of the most recent course of radiation therapy while at least 3 weeks must have elapsed since the completion of a non-nitrosourea containing chemotherapy regimen and at least 6 weeks since the completion of a nitrosourea containing chemotherapy regimen * Patients must have a Karnofsky performance status \>= 60% (i.e. the patient must be able to care for himself/herself with occasional help from others) * White blood cell (WBC) \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST)/ alanine aminotransferase (ALT) =\< 3 × institutional upper limit of normal * Creatinine within normal institutional limits OR * Creatinine clearance \>= 60 ml/min/1.73m\^2 for patients with creatinine levels above institutional normal * Patients must be able to provide written informed consent * Patients must have =\< 2 recurrences/relapses of their tumor * Women of childbearing potential must have a negative pregnancy test prior to study entry; cediranib has been shown to terminate fetal development in the rat, as expected for a process dependent on vascular endothelial growth factor (VEGF) signaling; women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Patients may not be breast-feeding a child * Patients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder; patients with prior malignancies must be disease-free for \>= five years * Patients must have a Mini-Mental State Exam score of \>= 15 * Patients must not have received prior cilengitide or cediranib therapy for their glioblastoma * ARM 1 OF THE DOSE EXPANSION COHORT ONLY, the last treatment regimen the patient received must have included anti-VEGF treatment; a period of at least 28 days must have elapsed since the last bevacizumab treatment or a period of at least 21 days since the last short-acting anti-VEGF treatment, before treatment with cediranib/cilengitide can begin ARM 2 OF THE DOSE EXPANSION COHORT ONLY: patients must not have had prior anti-VEGF therapy * Patients must not be on enzyme-inducing anti-epileptic drugs (EIAED); patients may be on non-enzyme inducing anti-epileptic drugs (NEIAED) or not be taking any anti-epileptic drugs Exclusion Criteria: * Patients with serious concurrent infection or medical illness, which would jeopardize the ability of the patient to receive the treatment outlined in this protocol with reasonable safety * Patients with \> 2 prior tumor recurrences/relapses * Patients receiving concurrent investigational agents; patients may not be receiving any other cancer related investigational agents * Although the following medications are not contraindicated on this study, each should be used with extreme caution due to potential nephrotoxic effects: vancomycin, amphotericin, pentamidine * Patients may not be on anti-coagulants (dalteparin, warfarin, etc) * Patients with a mean QTc \> 500 msec (with Bazett's correction) in screening electrocardiogram or history of familial long QT syndrome or other significant electrocardiogram (ECG) abnormality noted within 14 days of treatment are ineligible * Greater than +1 proteinuria on two consecutive dipsticks taken no less than 7 days apart; however, if the first urinalysis shows no protein, then a repeat urinalysis is NOT required * Patients with a New York Heart Association classification of III or IV * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cediranib or cilengitide * Uncontrolled intercurrent illness including, but not limited to, hypertension (blood pressure \> 140/90 mm Hg), ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because cediranib is a VEGF inhibitor with known abortifacient effects; breastfeeding should be discontinued if the mother is treated with cediranib * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with cediranib * Patients on enzyme-inducing AED (EIAED) are not eligible for treatment on this protocol; patients previously treated with EIAED may be enrolled if they have been off the EIAED for 14 days or more prior to the first dose of cediranib or cilengitide * Patients whose MRI scan demonstrates intratumoral hemorrhage or peritumoral hemorrhage are not eligible for treatment if deemed significant by the treating physician * Patients must not have a known coagulopathy that increases risk of bleeding or a history of clinically significant hemorrhages in the past * Patients receiving concurrent VEGF inhibitors are prohibited from participating in this study * Patients with conditions requiring concurrent drugs or biologics with proarrhythmic potential