This is a Phase 1, open-label study to evaluate the safety, tolerability, and pharmacokinetics of TAS-102 in patients with advanced solid tumors with varying degrees of renal impairment. The study is conducted in 2 parts: the Pharmacokinetic Part (Cycle 1) and the Extension Part (Cycles 2 and beyond). Patients may continue to receive treatment with TAS-102 during the study extension part only after completion of the Pharmacokinetic Part.