The goal of this clinical research study is to learn if the combination of topotecan and pazopanib can help to control recurrent cervical cancer. The safety of the study drug combination will also be studied.

Study Drug Administration:

If you are found to be eligible to take part in this study, you will receive the study drugs in 28-day study cycles.

You will take pazopanib every day for 28 days. You will take topotecan at about the same time every day on Days 1-21, but not take it on Days 22-28.

You should not take pazopanib 1 hour before or within 2 hours after eating. The pazopanib tablets should be swallowed whole with about a cup (8 ounces) of water.

You should not chew, crush, dissolve, or divide either the topotecan or the pazopanib tablets.

You will be given a study drug diary in which you will write information about when you take the study drug each time and how much you took. You will bring this diary to every study visit.

Study Visits:

On Day 1 of each cycle:

• You will have a physical exam. This will include a pelvic exam every 2 cycles.
• Blood (about 2 tablespoons) and urine will be collected for routine tests.
• Blood (about 2 tablespoons) will be collected for biomarker testing (Cycles 1 and 2 only), including genetic biomarkers. Biomarkers are found in the blood/tissue and may be related to your reaction to the study drug.
• If you can become pregnant, you will have a urine pregnancy test.

If you are taking warfarin, blood (about 2 tablespoons) will be drawn to check your blood's ability to clot. This will be done weekly during Cycle 1 and on any cycle after which you change your dose of warfarin or one of the study drugs.

On Day 1 of every even-numbered cycle (Cycles 2, 4, 6, and so on), you will have a CT scan or MRI of your abdomen and pelvis to check the status of the disease. You will also have an x-ray or CT scan of the chest to check the status of the disease as needed.

If the disease appears to be getting better at any time while you are taking the study drug, blood (about 2 tablespoons) will be drawn for biomarker testing.

If the study doctor thinks you are responding to the study drugs, blood (about 2 tablespoons) will be drawn on Day 1 of Cycle 6. If you leave the study before then, this sample will be drawn at that time.

End-of-Study Visit:

Within 4 weeks after your last dose of study drugs:

• You will have a physical exam.
• Blood (about 2 ½ teaspoons) will be drawn for routine tests.
• You will have a chest x-ray and either a CT scan or an MRI to check the status of disease.

If you are taking warfarin, blood (about 2 tablespoons) will be drawn to check your blood's ability to clot.

° If you stopped taking the study drug before Cycle 6 because the disease got worse, blood (about 2 tablespoons) will be drawn for biomarker testing.

Follow-Up Visits:

If you came off study for a reason other than the disease getting worse, you will be asked to return to the clinic for follow-up testing every 3 months. At these visits:

• You will have a physical exam.
• If the study doctor thinks it is needed, you will have a CT scan, MRI, or x-ray to check the status of the disease.

If the disease did get worse, you will be called every 3 months and asked about how you are doing. Each call should last about 5 minutes.

This is an investigational study. Pazopanib is FDA approved and commercially available for the treatment of advanced kidney cancer and certain types of advanced soft tissue sarcoma such as bone, cartilage, fat, or muscle. Topotecan is FDA approved and commercially available for the treatment of metastatic ovarian cancer that has returned after treatment and for the treatment of small cell lung cancer that has returned after first-line treatment. Topotecan is also FDA approved to treat advanced, recurrent or persistent carcinoma of the cervix in combination with cisplatin. The use of these drugs in combination is investigational. The study doctor can explain how the drugs are designed to work.

Up to 40 participants will be enrolled in this multicenter study. Up to 30 will take part at MD Anderson. Up to 10 will be enrolled at the Harris Health System.

Inclusion Criteria:

1. Patients must have histologically confirmed diagnosis of recurrent, persistent or advanced (stage IVB) squamous, adenocarcinoma or adenosquamous cervical cancer.
2. Eastern Cooperative Oncology Group (ECOG) performance status of </= 2.
3. Measurable disease criteria as defined by RECIST 1.1 criteria, measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded). Each lesion must be greater than or equal to 10 mm when measured by CT, MRI or caliper measurement by clinical exam; or greater than or equal to 20 mm when measured by chest x-ray. Lymph nodes must be greater than or equal to 15 mm in short axis when measured by CT or MRI.
4. Patients with persistent or recurrent disease must have received definitive chemoradiation therapy as first line therapy. Patients with advanced (stage IVB) disease may have received palliative radiation therapy.
5. Patients may have received one prior chemotherapy regimen for recurrence or progression. Cisplatinum with concurrent radiation does not count as a prior chemotherapy. Prior treatment with bevacizumab is allowable.
6. Patients must have adequate: Bone Marrow Function: Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl. Platelets greater than or equal to 100,000/mcl. Hemoglobin greater than or equal to 9 g/dL. Blood coagulation parameters: PT such that the international normalized ratio (INR) is less than or equal to 1.2 x ULN (institutional upper limit of normal) (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) and a PTT less than or equal to 1.2 x ULN. Subjects receiving anticoagulant therapy are eligible if their INR is stable and PT/PTT therapeutic and within the recommended range for the desired level of anticoagulation. Hepatic function: Bilirubin less than or equal to 1.5 x ULN AST and ALT less than or equal to 2.5 x ULN and alkaline phosphatase less than or equal to 2.5 x ULN. Renal function: Creatinine less than or equal to 1.5 x ULN.
7. Continue from #6. Urine Protein: If urine protein to creatinine ratio is greater than or equal to 1, a 24 hour urine protein must be assessed. Subjects must have a 24 hour urine protein value less than 1 g to be eligible. Use of urine dipstick for renal function assessment is not acceptable. Thyroid function: Patients must have normal baseline thyroid function tests (TSH, T3, T4). A history of hypothyroidism and/or hyperthyroidism is allowed, as long as the patient has stable well-controlled thyroid function for a minimum of 2 months. Neurologic function: Neuropathy (sensory or motor) less than or equal to grade 1.
8. Recovery from effects of recent surgery, radiotherapy, or chemotherapy Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated UTI). Any other prior therapy such as radiation therapy, tumor embolization, chemotherapy, immunotherapy, biologic therapy, investigational therapy or hormone therapy, must be discontinued at least 28 days prior to the first dose of pazopanib. At least 28 days must have elapsed since the patient underwent any major surgery (laparotomy, laparoscopy, thoracotomy, video assisted thorascopic surgery-VATS). No restriction on minor procedures (central venous access catheter placement, ureteral stent placement, thoracentesis).
9. Patients of childbearing potential must have a negative pregnancy test prior to the study entry and be practicing an effective form of contraception. Pregnant women are excluded from this study because of the potential for teratogenic or abortifacient effects.
10. Patients must have signed an approved informed consent and authorization form permitting the release of personal health information.
11. Patients must be greater than or equal to 18 years of age.
12. Patients must be capable of taking and absorbing oral medications. A patient must be clear of the following: Any lesion, whether induced by tumor, radiation or other conditions, which makes it difficult to swallow tablets Prior surgical procedures affecting absorption including, but not limited to major resection of stomach or small bowel. Active peptic ulcer disease. Malabsorption syndrome
13. Any concomitant medications that are associated with a risk of QTc prolongation and/or Torsades de Pointes should be discontinued or replaced with drugs that do not carry these risks, if possible. Patients who must take medication with a possible risk of Torsades de Pointes should be watched carefully for symptoms of QTc prolongation, such as syncope. Patients with personal or family history of congenital long QTc syndrome are NOT eligible.
14. Patients must meet pre-entry requirements.

Exclusion Criteria:

1. Patients who have had previous treatment with Pazopanib or Topotecan.
2. Prior malignancy. Note: Subjects who have had another malignancy and have been disease-free for 5 years, or subjects with a history of completely resected non-melanomatous skin carcinoma or successfully treated in situ carcinoma are eligible.
3. Central nervous system (CNS) metastases at baseline, with the exception of those subjects who have previously-treated CNS metastases (surgery +/- radiotherapy, radiosurgery, or gamma knife) and who meet both of the following criteria: a) are asymptomatic and b) have no requirement for steroids or enzyme-inducing anticonvulsants in prior 6 monthly time interval.
4. Clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding including, but not limited to: Active peptic ulcer disease.Known intraluminal metastatic lesion/s with risk of bleeding. Inflammatory bowel disease (e.g. ulcerative colitis, Crohn's disease), or other gastrointestinal conditions with increased risk of perforation. History of abdominal fistula, gastrointestinal perforation, or intra abdominal abscess within 28 days prior to beginning study treatment.
5. Clinically significant gastrointestinal abnormalities that may affect absorption of investigational product including, but not limited to: Malabsorption syndrome. Major resection of the stomach or small bowel.
6. Corrected QT interval (QTc) > 480 msecs.
7. History of any one or more of the following cardiovascular conditions within the past 6 months:Cardiac angioplasty or stenting. Myocardial infarction. Unstable angina. Coronary artery bypass graft surgery. Symptomatic peripheral vascular disease. Class III or IV congestive heart failure, as defined by the New York Heart Association (NYHA).
8. Uncontrolled hypertension [defined as systolic blood pressure (SBP) of >/= 140 mmHg or diastolic blood pressure (DBP) of >/= 90mmHg].
9. History of cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or untreated deep venous thrombosis (DVT) within the past 6 months. Note: Subjects with recent DVT who have been treated with therapeutic anti-coagulating agents for at least 6 weeks are eligible.
10. Major surgery or trauma within 28 days prior to first dose of investigational product and/or presence of any non-healing wound, fracture, or ulcer.
11. Evidence of active bleeding or pathologic conditions that carry high risk of bleeding such as known bleeding disorders, coagulopathy or tumor involving major vessels.
12. Recent hemoptysis (>/=½ teaspoon of red blood within 8 weeks before first dose of study drug).
13. Any serious and/or unstable pre-existing medical, psychiatric, or other condition that could interfere with subject's safety, provision of informed consent, or compliance to study procedures.
14. Unable or unwilling to discontinue use of prohibited medications for at least 28 days prior to the first dose of topotecan/pazopanib and for the duration of the study.
15. Administration of any non-oncologic investigational drug within 30 days prior to receiving the first dose of topotecan/pazopanib.
16. Any ongoing toxicity from prior anti-cancer therapy that is > grade 1 and/or that is progressing in severity, except alopecia.
17. Known HIV positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Pazopanib.
18. Patients who are pregnant or nursing are ineligible.