This is a phase I study of the combination of volasertib and romidepsin in patients with relapsed/refractory peripheral T cell lymphoma (PTCL) or stage IIB-IV cutaneous T cell lymphoma (CTCL). This study will determine the maximum tolerated dose (MTD) of this combination by treating cohorts of patients at a certain dose combination. The investigators will use a Bayesian design to determine the dose combination for the next cohort of patients and to determine the MTD. Overall response rate as well as adverse events will be monitored and reported.