Sorafenib and Bevacizumab to Treat Ovarian, Fallopian and Peritoneal Cancer

* ELIGIBILITY CRITERIA: Histopathologically documented recurrent/refractory epithelial ovarian cancer, primary peritoneal cancer or fallopian tube cancer from a previous biopsy verified by the Laboratory of Pathology, National Cancer Institute (NCI). -Recurrent/refractory disease defined as progression within 6 months of upfront platinum-containing therapy or progression after subsequent therapy in previously relapsed patients. Disease amenable to percutaneous or skin biopsy as determined by an associate investigator and a member of the interventional team. Patient willingness to have biopsies performed. Measurable disease defined as tumor greater than or equal to 1 cm. Age greater than or equal to 18 years. Life expectancy of more than 3 months. Performance status of 0 to 1 according to the Eastern Cooperative Oncology Group (ECOG) criteria. Adequate organ function as defined below: Laboratory Test Required value * Leukocytes greater than or equal to 3,000/ microliter * Absolute neutrophil count greater than or equal to 1,200/ microliter * Platelets greater than or equal to 100,000/ microliter * Total bilirubin less than or equal to 1.5 times the institutional upper limits of normal * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) less than or equal to 2.5 times the institutional upper limit of normal * Creatinine less than or equal to 1.5 mg/dL OR * Creatinine clearance greater than or equal to 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal. * Activated partial thromboplastin time (PTT) less than 1.5 times the institutional upper limits of normal * Prothrombin Time (PT)/ International normalized ratio (INR) less than 1.5 times the institutional upper limits of normal * Amylase and Lipase Less than institutional upper limits of normal Patients must have a urine protein/creatinine ratio (UPC) less than 1.0 for enrollment. No surgery, radiation therapy, chemotherapy, immunotherapy, biotherapy, or hormonal therapy (exception raloxifene for bone health) within four weeks (6 weeks for mitomycin C, carboplatin, or nitrosoureas); No metabolically active complimentary or alternative therapy for at least 1 week, defined as any ingested or administered chemical substances including herbal medications, but not including acupuncture, hypnosis, meditation, or other non-chemical treatments. No monoclonal antibody therapy for at least 6 weeks. Patients must have recovered from any acute toxicity related to prior therapy, including surgery. Toxicity should be less than or equal to grade 1 (as defined by Common Terminology Criteria for Adverse Events (CTCAE v3) or returned to baseline. Peripheral neuropathy less than or equal to grade 2 will be allowed as this patient population has universally been treated with platinum-based chemotherapy with residual neuropathy being a common occurrence. No other invasive malignancies within the past two years (with the exception of non-melanoma skin cancers, non-invasive bladder cancer, stage I endometrial cancer or cervical cancer synchronous to the ovarian cancer diagnosis and cured by surgical resection). Ability to understand and sign an informed consent form. Patients who require hematopoietic growth factor support (e.g. epogen, darbepoetin), Non-steroidal anti-inflammatory drugs (NSAIDs), and other maintenance medications prior to study entry will be allowed to continue their supportive therapies. Ability to tolerate orally administered medications. Contraception is not a consideration as these patients have all had surgical removal of their reproductive organs. Pregnant women are excluded from this study because BAY 43-9006 and bevacizumab are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with BAY 43-9006 and/or bevacizumab, breastfeeding should be discontinued if the mother is treated with BAY 43-9006 and/or bevacizumab. There is no limit on the number of prior regimens with which a patient has been treated. Patients who have been treated with bevacizumab previously are eligible for the trial if they have progressed while on bevacizumab-based therapy. -Disease progression on bevacizumab therapy will be defined as documented increase in disease based on imaging while the patient is receiving bevacizumab or within three months of their last dose of bevacizumab. Patients must be at least 6 weeks from their last dose of bevacizumab prior to being enrolled on study. Patients who have a healed fistula greater than 28 days prior to enrollment are eligible (refer to section 3.2.15 for patients who have had prior bevacizumab) EXCLUSION CRITERIA: Serious non-healing wounds (including wounds healing by secondary intention), acute or non-healing ulcers, or bone fractures within 3 months of enrollment. Moderate or massive hemoptysis or surgery within 28 days of enrollment. Ongoing treatment with any other investigational agents. Brain metastases * Patients with central nervous system (CNS) metastases within the past 2 years are ineligible. Patients who have had CNS disease curatively treated and without recurrence for 2 years may be eligible. but any CNS disease that has not undergone curative therapy with radiation, gamma knife, and/or surgical therapy are ineligible. * CNS imaging will not be mandated for all patients. However, if there is clinical suspicion of CNS involvement, a contrast computed tomography (CT) or magnetic resonance imaging (MRI) of the brain will be required. * Patients with CNS metastases may not be on steroids for the purpose of CNS disease or edema control. * Patients with CNS disease must be on an anti-seizure medication and that medication cannot be a CYPP4503A modulating agent. 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. Fully treated deep vein thrombosis no longer requiring anticoagulation will be allowed. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (American Heart Association (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 will become eligible for reconsideration 7 days after completing antibiotic therapy. Human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with sorafenib, bevacizumab, and/or the combination. Hypertension defined as systolic blood pressure greater than 150 mmHg or diastolic pressure greater than 90 mmHg despite optimal medical management. Therapeutic anticoagulation with coumadin, heparins, or heparinoids. Evidence of a bleeding diathesis. History of high grade varices or arteriovenous malformations. Patients previously treated with sorafenib will not be eligible for this trial. Fistula or bowel obstruction or perforation in the 28 days prior to enrollment. Patients must not be taking the cytochrome p450 (CYP450) enzyme-inducing drugs phenytoin, carbamazepine, phenobarbital, St. John's wort, or rifampin. For patients who have been previously treated with bevacizumab, any severe toxicity associated with bevacizumab while the patient was being treated with the agent will make the patient ineligible for the trial. This includes bevacizumab-induced hypertensive crisis, arterial thromboembolic events (including cardiac ischemia or cerebrovascular ischemia or other arterial thrombosis), nephrotic syndrome, gastrointestinal perforation, serious hemorrhage, and fistulas (unless the fistula completely resolved while the patient was still on bevacizumab or it has been surgically corrected).