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