Phase 1 will identify the maximum tolerated dose (MTD) or the highest protocol-defined dose in absence of exceeding the MTD, of the combination regimen of mogamulizumab and nivolumab subjects. Phase 1 will enroll up to 12 subjects. Phase 2 will explore the safety, efficacy and anti-tumor activity of the highest tolerated dose of the combination regimen. Phase 2 will enroll up to 184 subjects.