Sunitinib or Cediranib for Alveolar Soft Part Sarcoma

* INCLUSION CRITERIA: Status Update: Patients enrolled after Amendment G (version dated 08/16/2013), will be evaluated and compared to the first 13 patients by the study statistician and the Principal Investigator. * Patients must have histologically confirmed metastatic alveolar soft part sarcoma that is not curable by surgery. Diagnosis of malignancy must be confirmed by the department of pathology at the institution where the patient is enrolled prior to patient enrollment. * Patients must show evidence of objective disease progression per Response Evaluation Criteria in Solid Tumors (RECIST)v 1 on scans within the 6-month period immediately preceding enrollment. Both scans used to determine disease progression should have been obtained within this 6-month period. * Patients with newly diagnosed, unresectable, metastatic, and measurable alveolar soft part sarcoma (ASPS) who show clinical evidence of disease progression (including history and increasing physical symptoms) will also be eligible. On-study documentation will include a physician's rationale that supports evidence of clinical disease progression (i.e., increasing tumor pain). * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as greater than or equal to 20 mm with conventional techniques or as greater than or equal to 10 mm with spiral computed tomography (CT) scan. * Any prior therapy must have been completed greater than or equal to 4 weeks prior to enrollment on protocol and the participant must have recovered to eligibility levels from prior toxicity. Patients should be at least 6 weeks out from nitrosoureas and mitomycin C. Prior radiation should have been completed greater than or equal to 4 weeks prior to study enrollment and all associated toxicities resolved to eligibility levels. Patients who have had prior monoclonal antibody therapy must have completed that therapy at least 3 half-lives of the antibody or 6 weeks ago. Patients who have received more than a cumulative dose of 350 mg/m(2) of doxorubicin may be enrolled at the discretion of the Coordinating Center PI after consultation with a cardiologist and if screening echocardiogram is normal. * Patients must be greater than or equal to 2 weeks since any investigational agent administered as part of a Phase 0 study (also referred to as an early Phase I study or pre-Phase I study where a sub-therapeutic dose of drug is administered) at the Coordinating Center principal investigator (PI's) discretion and should have recovered to eligibility levels from any toxicities. * Patients with no prior therapy are eligible, provided they have metastatic disease that is not curable by surgery. * Age greater than or equal to 16 years. Patients age 16-17 years are eligible only if they have a BSA greater than or equal to 1.7 m(2) or weigh greater than or equal to 60 kg. * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2. * Life expectancy of greater than 3 months. * Patients must have normal organ and marrow function as defined below: * leukocytes greater than or equal to 3,000/mcL * absolute neutrophil count 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 * total serum bilirubin within normal institutional limits * aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamate-pyruvate transaminase (SGPT) less than or equal to 2.5 times institutional upper limit of normal * creatinine within normal institutional limits OR * creatinine clearance greater than or equal to 60 mL/min for patients with creatinine levels above institutional normal * QT corrected for heart rate (QTc) \<480 msec (with Bazett's correction) in screening electrocardiogram. * The following groups of patients are eligible after consultation with a cardiologist and at the Coordinating Center PI's discretion, provided they have New York Heart Association Class II (NYHA) cardiac function on baseline echocardiogram (ECHO): * those with a history of Class II heart failure who are asymptomatic on treatment * those with prior anthracycline exposure greater than a cumulative dose of 350 mg/m(2) * those who have received central thoracic radiation that included the heart in the radiotherapy port. * Patients must have blood pressure (BP) no greater than 140 millimeters of mercury (mmHg) (systolic) and 90 mmHg (diastolic) for eligibility. Initiation or adjustment of BP medication is permitted prior to study entry provided that the BP reading prior to enrollment is no greater than 140/90 mmHg. * Left ventricular ejection fraction (LVEF) greater than or equal to institutional lower limit of normal. * Because sunitinib is metabolized primarily by the cytochrome P450 3A4 (CYP3A4) liver enzyme, strong CYP3A4 inhibitors are not permitted within 7 days before and during the study, and strong CYP3A4 inducers are not permitted within 12 days before and during the study. A list of drugs that may interact with the cytochrome P450 system is included in Appendix C. Every effort should be made to switch patients taking such agents or substances to other medications 1 week prior to starting therapy, particularly patients with brain metastases who are taking enzyme- inducing anticonvulsant agents (Appendix D). Patients who require potent CYP3A4 inducers or inhibitors and cannot switch medications must have their case reviewed by the Coordinating Center PI and may be enrolled only after discussion with and agreement from the Coordinating Center PI. Current clinical studies with cediranib have not found clinically significant effects on cediranib pharmacokinetic (PK) with co-administration of CYP3A4 inducers or inhibitors. Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics (PK) of cediranib will be determined following review of their case by the Coordinating Center PI. * Both study agents have been shown to terminate fetal development in the rat, as expected for a process dependent on VEGF signaling. For this reason, women of childbearing potential must have a negative pregnancy test prior to study entry. Women of child-bearing potential and men must agree to use two reliable forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 2 months following study drug discontinuation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Patients who are nursing infants: because there is an unknown but potential risk for adverse events (AEs) in nursing infants secondary to treatment of the mother with study agents, breastfeeding should be discontinued if the mother is treated with the study agents. * Ability to understand and the willingness to sign a written informed consent document. * Patients must be able to swallow whole tablets and capsules. EXCLUSION CRITERIA: * Patients must not have received prior treatment with any VEGF receptor tyrosine kinase inhibitor (e.g., cediranib, sunitinib, pazopanib, sorafenib); however, prior treatment with bevacizumab is allowed. * Patients may not be receiving any other investigational agents. * Major surgery within 4 weeks prior to entry into the study, or a surgical incision that is not fully healed. * History of familial long QT syndrome, or use of medications that may cause QTc interval prolongation. * Patients with a pre-existing thyroid abnormality who are unable to maintain thyroid function in the normal range with medication are ineligible. * Warfarin and its derivatives are not allowed. Patient can be receiving low molecular weight heparin if clinically indicated. * Uncontrolled intercurrent illness including, but not limited to hypertension, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Patients with any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow, retain, and/or absorb the drug are excluded. * Patients with any of the following conditions are excluded: serious or non-healing wound, ulcer; history of abdominal fistula, gastrointestinal perforation, or intra - abdominal abscess within 28 days of treatment; coronary/peripheral artery bypass graft or stenting within the past 12 months; or cerebrovascular accident (CVA) or transient ischemic attack within the past 12 months. * Greater than 2+ proteinuria on two consecutive dipsticks taken no less than 1 week apart or 24-hour urine protein of \> 1 g. Patients with \< 2+ proteinuria are eligible following initial determination by urinalysis within 1 week prior to enrollment and do not need the urinalysis repeated. * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for PK interactions with cediranib or sunitinib. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.