The goal of this clinical research study is to find the highest tolerable combination dose of bendamustine and bevacizumab that can be given to patients with advanced cancer. The safety of the drug combination will also be studied.

The Study Drugs:

Bendamustine is designed to damage DNA (the genetic material) of cancer cells. Bendamustine also interferes with the creation of new DNA, which may keep cancer cells from repairing themselves or forming new cancer cells.

Bevacizumab is designed to block the growth of blood vessels that supply the nutrients needed for tumor growth, which may prevent or slow down the growth of cancer cells. Bevacizumab is no longer FDA approved to treat breast cancer.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of bendamustine based on when you join this study. Up to 4 dose levels of bendamustine will be tested. Up to 3 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of bendamustine is found.

All participants will receive the same dose level of bevacizumab.

Study Drug Administration:

You will receive bendamustine by vein over 30-60 minutes on Days 1 and 2 of each 28-day study cycle.

You will receive bevacizumab by vein on Days 1 and 15 of each cycle. The first time you receive bevacizumab, it will be given over 90 minutes. If you tolerate it well, the rest of the doses will be given over 30-60 minutes.

Study Visits:

On Day 1 of each cycle:

• You will have a physical exam, including measurement of your weight and vital signs.
• Blood (about 1 tablespoon ) will be drawn for routine tests.
• Women who are able to become pregnant will have a urine pregnancy test.

Every 2 cycles (Cycles 2, 4, 6, and so on):

• Blood (about 1 tablespoon) will be drawn to test for tumor markers.
• A chest x-ray, CT scan, MRI scan, PET scan, and/or PET/CT scan will be performed to check the status of the disease. These scans will also be performed at any time that the doctor thinks it is needed to check the status of the disease. If the study doctor thinks it is in your best interest, other types of scans that have not been listed here may also be performed.

Length of Study:

You may continue taking the study drug combination for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug if the disease gets worse or intolerable side effects occur.

Follow-Up Visit:

Six (6) weeks after you stop taking the study drug combination for any reason, the following tests and procedures will be performed:

• You will have a physical exam.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) will be drawn for routine tests.
• If the study doctor thinks it is needed, a chest x-ray, CT scan, MRI scan, PET scan and/or PET/CT scan will be performed to check the status of the disease. If the study doctor thinks it is in your best interest, other types of scans that have not been listed here may also be performed.

This is an investigational study. Bendamustine is FDA approved and commercially available for the treatment of chronic lymphoid leukemia and non-Hodgkin's lymphoma. Bevacizumab is FDA approved and commercially available for the treatment of metastatic colorectal cancer, non-small-cell lung cancer (NSCLC), and a type of brain cancer called glioblastoma multiforme. The use of these drugs in combination in advanced cancer is investigational.

Up to 55 participants will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

1. Patients must have histologically confirmed cancer.
2. Patients should be refractory to standard therapy, relapsed after standard therapy, or have no standard therapy that increases survival by at least 3 months.
3. Performance status Eastern Cooperative Oncology Group (ECOG) 0-2 (capable of all self care but unable to carry out any work activities). Pediatric: performance status Karnovsky (>10) or Lansky (<10).
4. Adequate renal function (serum creatinine </= 2.0 mg/dL or the calculated Glomerular Filtration Rate (GFR) >/= 40 mL/min if creatinine > 2.0 mg/dL). Pediatric: serum creatinine </= 1.5 mg/dL or 2x upper limit of normal, for age.
5. Hepatic function: total bilirubin </= 1.0 mg/dL (Patients with Gilbert's Syndrome must have a total bilirubin </= 3.0 mg/dL); ALT </= 3 times upper limit of normal. If patient has liver metastases, total bilirubin </= 5 mg/dL; ALT </= 5 times upper limit of normal.
6. Adequate bone marrow function (Absolute neutrophil count (ANC) >/= 1,000 cells/uL; Platelets (PLT) >/= 75,000 cells/uL), unless these abnormalities are due to bone marrow involvement.
7. At least three weeks from previous cytotoxic chemotherapy. After targeted or biologic therapy there should be 5 half-lives or 3 weeks, whichever is shorter.
8. All females in childbearing age MUST have a negative urine human chorionic gonadotropin (HCG) test unless prior hysterectomy or menopause (defined as age above 55 and six months without menstrual activity). Patients should not become pregnant or breast-feed while on this study. Sexually active patients should use effective birth control.
9. Must be >/= 13 years of age.
10. Sign informed consent. Pediatric participants: age 13-17 would sign assent, parent or guardian would sign consent.

Exclusion Criteria:

1. Pregnant females.
2. Inability to complete informed consent process and adhere to protocol treatment plan and follow-up requirements.
3. Serious or non-healing wound, ulcer or bone fracture.
4. Uncontrolled systemic vascular hypertension (systolic blood pressure > 140 mm Hg, diastolic blood pressure > 90 mm Hg).
5. Uncontrolled intercurrent illness, including, but not limited to, ongoing or active infection requiring parental antibiotics, or psychiatric illness/social situations that would limit compliance with study requirements.
6. History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days.
7. Patients with clinical bleeding, active gastric or duodenal ulcer.
8. Patients with history of bleeding central nervous system (CNS) metastasis will be excluded from the trial.
9. Patients with major surgery within 28 days prior to entering the study.