This is a Phase Ib, open-label, multi-center, dose-escalation study of orally administered tivozanib in combination with capecitabine to approximately 24 subjects with advanced solid tumors and, in the expanded MTD cohort, subjects with locally advanced or metastatic breast or colorectal cancer. This study is designed to evaluate the safety, tolerability, dose-limiting toxicities, maximum tolerated dose, pharmacokinetic, and antineoplastic activity. The number of cohorts evaluated and the maximum doses to be administered will depend upon the observed tolerability. Dose level "0", tivozanib HCl 1.5 mg and capecitabine 1000 mg/m² BID, is the starting dose level. Once assigned to a cohort, each subject will continue to be treated at the same dose level and schedule throughout the course of the study.