Inclusion Criteria: - Adult patients, >/= 18 years of age - Interval of at least 12 weeks from completion of adjuvant radiotherapy for gliomas to study entry - Karnofsky Performance Status of >/= 70 at screening - Confirmed measurable disease per RANO - Adequate hematologic and organ function Patients enrolled in Stage 1: - Histologically documented recurrent or progressive high-grade gliomas (WHO Grade III-IV) - Prior treatment with at least one regimen for gliomas (radiotherapy with or without chemotherapy for Grade III gliomas and radiotherapy with chemotherapy for Grade IV gliomas) and/or not considered to be a candidate for regimens known to provide clinical benefit Patients enrolled in Stage 2: - Histologically documented recurrent or progressive glioblastoma (WHO Grade IV gliomas) - Prior treatment with one or two regimens for glioblastoma (with the initial regimen consisting of radiotherapy with chemotherapy) Exclusion Criteria: - Treatment with anti-tumor therapy (approved or experimental) within 4 weeks prior to initiation of study drug - Requirement for anticoagulants such as warfarin or any other warfarin-derivative anticoagulants; low-molecular-weight heparin is permitted - Any contraindication to MRI examination - Evidence of Grade >/= 1 intracranial hemorrhage - Active congestive heart failure or ventricular arrhythmia requiring medication - Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse or cirrhosis - Unresolved toxicity from prior therapy with the exception of lymphopenia (for patients with prior temozolomide) and alopecia - Pregnant or lactating women