The main purpose of this study is to learn more about the safety of an investigational drug, axitinib. An investigational drug is a drug that has not been approved by the Food and Drug Administration (FDA) and is available for research use only. Researchers will also see what changes happen to the tumors while taking the axitinib and after it is stopped (during the scheduled breaks), and what changes in the tumor may be responsible for this growth. This will be done by using a special kind of scan called an 18F-FLT PET/CT. This scan is considered an investigational type of scan and is not used for clinical care. These scans are not approved by the FDA, their use in this study is just for research purposes.

In addition, the investigators want to find out how the drug is processed and distributed in the human body. The investigators will also look at how different types of cancer are affected by axitinib.

Inclusion Criteria:

• Patients must have histologically or cytologically confirmed solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which no standard therapy exists.
• Patients must have measurable disease
• Must be >/= 18 years of age
• All patients need to be willing to undergo planned pharmacodynamic assessments, including serial PET imaging, plasma markers, and pharmacokinetic sampling.

Exclusion Criteria:

• Patients who have had chemotherapy, radiotherapy, experimental therapy or major surgery within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered (to grade -Patients may not be receiving any other investigational agents.
• Patients with prior anti-VEGF directed therapy may be allowed only if approved by the PI and greater than 8 weeks since last exposure
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to axitinib
• Patients with poorly controlled hypertension
• Patients who require use of therapeutic doses of coumarin-derivative anticoagulants
• Patients with any condition that impairs their ability to swallow and retain axitinib tablets are excluded.
• Patients with any of the following conditions are excluded: Serious or nonhealing wound, ulcer, or bone fracture; History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of treatment; Any history of cerebrovascular accident (CVA) or transient ischemic attack within 12 months prior to study entry; History of myocardial infarction, cardiac arrhythmia, stable/unstable angina, symptomatic congestive heart failure, or coronary/peripheral artery bypass graft or stenting within 12 months prior to study entry; History of pulmonary embolism within the past 12 months; Class III or IV heart failure as defined by the NYHA functional classification system.
• Patients without appropriate lesion on CT scan for FLT-PET/CT imaging
• CYP3A4 inducers/inhibitors medications will be reviewed by the Principal Investigator.
• Steroid use is not recommended during axitinib treatment
• Patients with a pre-existing thyroid abnormality who are unable to maintain thyroid function in the normal range with medication are ineligible.
• Patients with known brain metastases should be excluded
• HIV-positive patients on combination antiretroviral therapy are ineligible