Inclusion Criteria: - Histologic diagnosis of glioblastoma (GBM), gliosarcoma, anaplastic astrocytoma (AA), anaplastic oligodendroglioma (AO), or anaplastic mixed oligoastrocytoma (AOA). Patients are eligible if the original histology was lower-grade glioma. - Patients must have supratentorial disease without infratentorial involvement. - Unequivocal progression by MRI or CT - Patients with recurrence who undergo resection and are left without measurable or evaluable disease are eligible. - Patients must have recurrent disease and may have had any number of prior relapses (including no prior relapses). Relapse is defined as progression following initial therapy. - 18 years of age or older - Life expectancy of greater than 8 weeks - Karnofsky performance status of 60 or greater - Normal organ and marrow function as outlined in the protocol - Protocol treatment must begin within 5 consecutive days after registration - Patients enrolled in Part 2 must be willing to undergo surgical resection and have pre-treatment archival tumor tissue available for molecular analysis - Women of child-bearing potential must have a negative serum or urine pregnancy test within 72 hours before the start of the investigational product. In addition, women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of the study participation. - Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: - Patients who have had prior chemotherapy within the past 4 weeks (6 weeks for nitrosoureas or mitomycin C) or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Patients who received non-cytotoxic drug therapy must be off treatment for at least 2 weeks. - Patients who have received any form of cranial radiation within 3 months of study entry. - Major surgical procedure (including craniotomy) or significant traumatic injury less than 28 days or those who receive minor surgical procedures (e.g. core biopsy or fine needle aspiration) within 7 days. - Patients may not be receiving any other investigational agents within the past 28 days. - Patients who have had prior therapy with CXCR4 inhibitors or anti-VEGF targeted agents. Prior therapy with thalidomide and lenalidomide is allowed. - Patients who have received prior treatment with implanted radiotherapy or chemotherapy sources such as wafers of polifeprosan 20 with carmustine. - History of allergic reactions attributed to compounds of similar chemical or biologic composition to plerixafor or bevacizumab. - Patients requiring therapeutic anticoagulation with warfarin at baseline are excluded. However, therapeutic or prophylactic therapy with a low-molecular weight heparin at baseline is acceptable. - Patients must not have a known coagulopathy that increases risk of bleeding or a history of clinically significant hemorrhages in the past. - Patients whose MRI scan demonstrates intratumoral hemorrhage or peritumoral hemorrhage are not eligible for treatment if deemed significant by the treating physician. - Patients with gastrointestinal bleeding or any other hemorrhage/bleeding event CTCAE Grade > 3 within 30 days prior to study entry. - Uncontrolled intercurrent illness including but not limited to 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. - Patients with greater than 1+ proteinuria on a urine dipstick or equivalent routine laboratory analysis will require further testing with a urine protein to creatinine ratio. - History of non-healing wounds or ulcers, or bone refractures within 3 months of fracture - HIV-positive patients on combination antiretroviral therapy - Participants with a history of a different malignancy are ineligible except for the following circumstances: Individuals with a history of other malignancies are eligible if they have been disease-free for at least 3 years AND are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 3 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin. - Pregnant women - Men or women of childbearing potential who are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for up to 2 weeks after the last dose of study drug.