Plerixafor (AMD3100) and Bevacizumab for Recurrent High-Grade Glioma

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. * 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) on NON-anti-VEGF(R) containing regimens. Relapse is defined as progression following initial therapy. For patients who progressed on a prior anti-VEGF(R) containing regimen including bevacizumab, only one prior relapse on an anti-VEGF(R) containing regimen is allowed. * 18 years of age or older * Karnofsky performance status of 60 or greater * Normal organ and marrow function as outlined in the protocol * Ability to understand and willingness to sign a written informed consent document. * Protocol treatment must begin within 5 consecutive days after registration * Patients enrolled in Part 2 must be willing to undergo surgical resection and have sufficient 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, female subjects of child-bearing potential and male subjects with partners of child-bearing potential must agree to use an effective means of birth control while on study therapy and for a minimum of 4 months following last plerixafor dose and 6 months following last bevacizumab dose. Effective birth control includes: * birth control pills, depot progesterone, or an intrauterine device plus one barrier method; * or 2 barrier methods. Effective barrier methods are male and female condoms, diaphragms, and spermicides (creams or gels that contain a chemical to kill sperm). Hormonal contraceptive methods are not sufficient, as information about any interaction of plerixafor with hormonal contraceptives is not known. Exclusion Criteria: * Patients who have had prior chemotherapy within the past 4 weeks (6 weeks for nitrosoureas or mitomycin C). Patients must be off treatment with Temozolomide for at least 23 days. Patients who received non-cytotoxic drug therapy must be off treatment for at least 2 weeks. For patients enrolling in Part 1 or Part 3 AND who have progressed on a prior bevacizumab-containing regimen, patients may continue treatment with bevacizumab 10 mg/kg monotherapy, with last dose of bevacizumab administered no fewer than 14 days from start of Plerixafor and bevacizumab. For participants enrolling in Part 1 or Part 3 AND who have progressed on a prior anti-VEGF(R) (other than bevacizumab) containing regimen, patients must be off anti-VEGF(R) treatment for at least 28 days before receiving Plerixafor and bevacizumab. For patients enrolled in Part 2 (surgical substudy) AND who have progressed on a prior bevacizumab or other anti-VEGF(R) containing regimen, patients must be off anti-VEGF(R) treatment for at least 28 days prior to surgery. NOTE: Participants must have recovered to a grade 0 or 1 from any clinically significant toxicity related to prior therapy (with the exception of lymphopenia, which is common after therapy with temozolomide). For any patient who received prior bevacizumab or an anti-VEGF(R) therapy, patient must NOT have discontinued that treatment regimen due to a treatment-related toxicity. * In order to prevent registering patients with pseudoprogression rather than true disease progression, patients must not have received any form of cranial radiation within 12 weeks of study entry. NOTE: Patients who have received cranial radiation within 12 weeks of study entry will be allowed to register to trial only if progressive disease is confirmed via biopsy. * 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. NOTE: If agent's half-life x 5 is \< 28 days, patient may have taken it within the last 28 days, provided at least 5 half-lives have passed since having last taken it. * Patients who have had prior therapy with CXCR4 inhibitors. * Patients with one prior relapse on a bevacizumab or an anti-VEGF(R) (i.e. VEGF-trap, vandetanib, cediranib, sunitinib, sorafenib, XL184, etc.) containing regimen are allowed to participate. * 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 (e.g. Gliadel wafers). * History of allergic reactions attributed to compounds of similar chemical or biologic composition to plerixafor or bevacizumab. * For the first 20 patients to register, no anti-coagulation is allowed; for all subsequent patients screened, patients requiring therapeutic anticoagulation with warfarin at baseline are excluded (however, therapeutic or prophylactic therapy with a low-molecular weight heparin 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 uncontrolled hypertension, 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 myocardial infarction, unstable angina, stroke, or TIA within 6 months prior to planned Day 1 of dosing * History of non-healing wounds or ulcers, or bone refractures within 3 months of fracture * History of abdominal fistula, gastrointestinal perforation, or intraabdominal abscess within 6 months prior to planned Day 1 of dosing * 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 and breastfeeding 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 a minimum of 4 months following last Plerixafor dose and 6 months following last bevacizumab dose.