Dasatinib in Combination With Bevacizumab to Treat Advanced Solid Tumors

* INCLUSION CRITERIA: * Patients must have a solid tumor malignancy that is metastatic or unresectable and for which standard curative therapies do not exist or are no longer effective. --Patients must have histological documentation of cancer confirmed in the Laboratory of Pathology/NCI. * Patients must be off prior chemotherapy, radiation therapy, hormonal therapy, or biological therapy for at least 4 weeks. Patients who were receiving mitomycin C, nitrosoureas, bevacizumab or carboplatin must be 6 weeks from the last administration of chemotherapy. Patients with prostate cancer must continue to receive LHRH agonist (unless orchiectomy has been performed). Patients should not be receiving complementary/alternative therapy while on study. Any patient who has undergone therapy with a monoclonal antibody must be at least 4 weeks from the last treatment. * All patients enrolling in group 2 must have at least one lesion deemed safe to biopsy and be willing to undergo the three mandatory biopsies. This determination will be made by a member of the interventional radiology team or surgical associate investigator and an associate investigator. This requirement is not necessary for patients in group 1. * Age \>=18 years. Because no dosing or adverse event data are currently available on the use of dasatinib in combination with bevacizumab in patients \<18 years of age, children are excluded from this study, but may be eligible for future pediatric phase 1 combination trials. * ECOG performance status 0 or 1. ECOG performance status of 2 will be considered on a case by case basis with a focused assessment on risk of perforation. * Life expectancy of greater than 3 months. * Patients must have adequate organ and marrow function as defined below: * Inclusion criteria laboratory values * Leukocytes \>3,000/microl * Hemoglobin \>= 10g/dl * Absolute neutrophil count \>1,200/microl * Platelets \>100,000/microl * total bilirubin \<=1.5 X institutional upper limits of normal in the absence of Gilbert's syndrome * AST(SGOT) and ALT(SGPT) \<=2.5 X institutional upper limit of normal * creatinine \<=1.5 mg/dL OR Creatinine clearance \>45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal. * Activated partial thromboplastin time (PTT) \<= 1.25 x institutional upper limits of normal in the absence of lupus anticoagulant * Prothrombin Time (PT) OR INR \<= 1.25 x institutional upper limits of normal * Spot Urine Protein Creatinine Ratio \<=0.5; If result is 0.5 or more, a 24-hour urine for protein excretion must be \<=1000mg * Patients must have recovered from toxicity related to prior therapy to at least CTEP grade 1 (defined by CTCAE 4.0). Chronic stable grade 2 peripheral neuropathy secondary to neurotoxicity from prior therapies may be considered on a case by case basis by the Principal Investigator. * As the effect of dasatinib and bevacizumab in combination on the developing human fetus is not known, women of child-bearing potential and men must agree to use adequate contraception (abstinence; hormonal or barrier method of birth control) for the study and at least 3 months after completion. Pregnant women will not be eligible for study. * Ability to understand and the willingness to sign a written informed consent document. * Evaluable disease or measurable disease of \>= 1 cm. * Patients may not have any clinically significant cardiovascular disease including the following: * myocardial infarction or ventricular tachyarrhythmia within 6 months * prolonged QTc \>=480 msec (Fridericia correction) * ejection fraction less than institutional normal * major conduction abnormality (unless a cardiac pacemaker is present) * Patients with any cardiopulmonary symptoms of unknown cause (e.g. shortness of breath, chest pain, etc.) should be evaluated by a baseline echocardiogram with or without stress test as needed in addition to electrocardiogram (EKG) to rule out QTc prolongation. The patient may be referred to a cardiologist at the discretion of the principal investigator. Patients with underlying cardiopulmonary dysfunction should be excluded from the study. EXCLUSION CRITERIA: * Brain metastases * Patients who have a history of remote CNS metastases that have undergone "curative therapy" by radiation therapy, gamma knife therapy, or surgery and have remained without recurrence for a period of \>=6 months will be eligible. * CNS imaging will not be mandated for all patients. However, if there is clinical suspicion of CNS involvement, a contrast CT or MRI of the brain will be required. Screening CNS scans should be required for certain tumor types with relatively high risk of CNS metastases, including but not limited to melanoma, renal cell carcinoma, breast, lung. * Thrombotic or embolic events within the past 6 months such as a cerebrovascular accident (including transient ischemic attacks), pulmonary embolism, unstable angina, or myocardial infarction. Patients with recent (\< 3 month history) of venous thrombotic events will be considered on a case by case basis. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (AHA Class II or worse), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Patients with evidence of active infection must have completed antibiotic therapy and be without clinical or laboratory evidence of infection for seven days after treatment has concluded. * QTc prolongation (defined as a QTc interval equal to or greater than 480 msecs) or other clinically significant EKG abnormalities * Patients may not have any clinically significant cardiovascular disease including the following: * Myocardial infarction or ventricular tachyarrhythmia within 6 months * Prolonged QTc \>= 480msec (Fridericia correction) * Ejection fraction less than institutional normal (should be done if clinically indicated and for patients with congestive heart failure on medication) * Major conduction abnormality (unless a cardiac pacemaker is present) * Patients who have an active pleural effusion may be considered if tapped prior to study. Patients with pleural effusions that are too small to be removed may be considered on a case by case basis. Patients with a Grade 2, asymptomatic pericardial effusion found incidentally on imaging studies may be considered on a case by case basis. * Dasatinib is metabolized primarily by the CYP3A4 liver enzyme. Consideration should be given to using alternative medications not impacting CYP3A4 while on dasatinib therapy. * Patients may not be receiving any prohibited potent CYP3A4 inhibitors. For these drugs, a wash-out period of \>= 7 days is required prior to starting dasatinib treatment. * Category I drugs that are generally accepted to have a risk of causing Torsades de Pointes. A wash-out period of \>= 7 days is required for the following drugs prior to starting dasatinib treatment: * Quinidine, procainamide, disopyramide * Amiodarone, sotalol, ibutilide, dofetilide * Erythromycin, clarithromycin * Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide * Cisapride, bepridil, droperidol, methadone, arsenic, chlorquine, domperidone, halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine * HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with dasatinib, bevacizumab, and/or the combination. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Patients who have been treated with dasatinib (or any other Src-family kinase inhibitors) will be excluded * Hypertension defined as systolic blood pressure \>140 mmHg or diastolic pressure \>= 90 mmHg despite optimal medical management. * Proteinuria defined as a spot urine analysis for protein creatinine ratio (UPC) of \> 1.0 * Therapeutic anticoagulation with coumadin, heparins, or heparinoids. Prophylaxis doses are permitted. * Serious non-healing wounds (including wounds healing by secondary intention), acute or non-healing ulcers, or bone fractures within 3 months of fracture. History of abdominal fistula, major surgery, bowel obstruction, or intra-abdominal abscesses within 28 days will be excluded. Any patient with history of gastrointestinal perforation will be excluded due to possibility of increased risk of perforation with bevacizumab. * Evidence of bleeding diathesis * Impairment of swallowing that would preclude administration of dasatinib. * History of hemoptysis or surgery within the past 28 days. * Patients with squamous cell carcinoma of the lungs will be excluded due to risk of fatal pulmonary hemorrhage. If a patient has a history of any type primary lung cancer and hemoptysis, they will be excluded. * History of high grade varices. * Use of herbal supplements are not permitted within 7 days of trial commencement and on study. Vitamin supplement (above a typical single multi-vitamin) usage is discouraged unless clearly indicated by an existing medical condition. An Associate or Principal Investigator will have the discretion regarding which vitamin supplements are permitted. * Known hypersensitivity to Chinese hamster ovary cell products or recombinant human antibodies. * Use of any other concurrent investigational agents for treatment or anticancer agents including hormonal therapy, except in the case of prostate cancer patients who are being treated with LHRH agonist at the time of trial entry * Pregnant women are excluded from this study because bevacizumab is an antibody to VEGF with the potential for teratogenic or abortifacient effects. Dasatinib is a potential teratogen. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother bevacizumab or dasatinib, breastfeeding should be discontinued if the mother is treated on this study.