Sorafenib + Topotecan for Platinum-Resistant Recurrent Ovarian Cancer

Inclusion Criteria: * Have histologically-confirmed epithelial ovarian cancer, primary peritoneal carcinomatosis or fallopian tube cancer. Enrollment of patients with clear cell histology is encouraged. * Have measurable disease according to RECIST or detectable disease by 1) CA-125 at least twice the ULN within 14 days prior to registration for protocol therapy; 2) Ascites and/or pleural effusion attributed to tumor; 3) solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST definitions for target lesions. * Have failed at least one prior platinum based chemotherapeutic regimen. * No more than 3 prior treatment regimens for epithelial ovarian cancer. * Prior radiation therapy is allowed to \< 25% of the bone marrow. * Be at least 4 weeks since last anti-cancer treatment, radiation or surgery at the time of registration for protocol therapy. * No active cancer in addition to the epithelial ovarian cancer within the last 5 years, with the exception of: superficial skin cancer (basal cell or squamous cell skin carcinoma; carcinoma in situ of the cervix; Stage I endometrial cancer with less than 50% invasion of the myometrium, or other adequately treated Stage I or II cancer in complete remission. * Age \> 18 years at the time of consent * Written informed consent and HIPAA authorization for release of personal health information. * Females of childbearing potential must be willing to use an effective method of contraception (hormonal or barrier method of birth control; abstinence) from the time consent is signed until 90 days after treatment discontinuation * Females of childbearing potential must have a negative pregnancy test within 7 days prior to being registered for protocol therapy. Exclusion Criteria: * No known or suspected allergy to sorafenib or any agent given in the course of this trial. * No prior treatment with anti-angiogenesis therapy. * No active CNS metastases. * No treatment with any investigational agent within 30 days prior to being registered for protocol therapy. * No concurrent combination anti-retroviral therapy for the treatment of immunodeficiency. * No clinically significant infections requiring antibiotic treatment. * No evidence of bowel obstruction, malabsorption, or other contraindication to oral medication. * No serious non-healing wound, ulcer, or bone fracture. * No major surgery, open biopsy or significant traumatic injury within 28 days of registration for protocol therapy. * No use of St. John's Wort or rifampin (rifampicin) while on protocol therapy. * No condition that impairs patient's ability to swallow whole pills.