Ph1 Volasertib Plus Romidepsin in R/R PTCL and CTCL

Inclusion Criteria: 1. A) Patients with a relapsed/refractory peripheral T cell lymphoma. Patients must have received at least one prior standard cytotoxic regimen such as CHOP or EPOCH OR B) Patients with relapsed/refractory stage IIb-IV cutaneous T cell lymphoma who have received at least one standard systemic treatment such as extracorporeal photopheresis, bexarotene or interferon. 2. Age \> 18 years old 3. Eastern Cooperative Oncology Group performance status of \<2 4. Evidence of measurable or evaluable disease 5. Patients must have recovered from all clinically relevant toxicities related to prior anticancer therapies to ≤ grade 2 (CTCAE v 4.03). Exception to this criterion: patients with any grade of alopecia are allowed to enter the treatment. 6. Platelets \>100 x 109/L 7. ANC\>1.5 x 109/L 8. AST/ALT \<3.0 x institutional ULN, except for people with liver involvement by their lymphoma, who may be included if AST/ALT \<5 x ULN. 9. Total Bilirubin \< 1.5 x ULN, except for patients with gilbert's syndrome who may be included if total bilirubin \< 3.0 x ULN and direct bilirubin \< 1.5 x ULN 10. The following laboratory values must be greater than the lower limits of normal prior to starting study drug (supplementation allowed): potassium, magnesium 11. Calculated or measured CrCl\> 30ml/min (Appendix: 3) 12. Ability to provide written informed consent for the protocol must be obtained prior to any screening procedures. If consent cannot be expressed in writing, it must be formally documented and witnessed, ideally via an independent trusted witness. 13. Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests and other procedures. Exclusion Criteria: 1. Prior Treatment: 1. Patients must not have received chemotherapy, radiation or surgical resection of malignancy within 3 weeks prior to the start of study drug. However, if they have received nitrosurea or mitomycin C then they should not be enrolled in the study until 6 weeks after therapy was last received. 2. No limitations to number of prior therapies. 3. Prior treatment with volasertib or any PLK1 inhibitor 4. Prior treatment with a histone deacetylase inhibitor (anti-epileptics ok) 2. Active, uncontrolled, serious infection or medical or psychiatric illness likely to interfere with participation in this clinic trial 3. Known HIV infection. 4. Active or chronic hepatitis B infection. 5. Clinical evidence of symptomatic progressive brain or leptomeningeal disease during the past 6 months. 6. Pregnant or breast feeding. Treatment under this protocol would expose an unborn child to significant risks. 7. Women and men of reproductive potential who are unwilling or unable to use an effective means of birth control during the study and for 3 months after receiving study drug. 8. Major surgery within the four weeks prior to initiating protocol therapy. 9. Diagnosis or treatment for any malignancy other than NHL within the 3 years preceding Day 1 of the protocol therapy. Exceptions are: 1. Basal or squamous cell carcinoma of the skin 2. In situ malignancy that has been completely resected. 3. Prostate cancer that was treated with prostatectomy or radiotherapy over 2 years before Day 1 of protocol therapy and whose PSA is undetectable. 10. Treatment with another investigational agent currently or within 21 days prior to enrollment. Patients may participate in other non-treatment studies concurrently if it will not interfere with participation in this study. 11. Myocardial infarction or unstable angina within 6 months prior to enrollment or has New York Hospital Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. 12. QTcF\>470msec using the Fredericia formula. 13. Known hypersensitivity to the trial drugs (volasertib and romidepsin) 14. Receiving medications that meet one of the following criteria and that cannot be discontinued at least 1 week prior to the start of treatment with study drug and for the duration of participation (see Appendix 2 Tables): 1. Medication with a significant known risk of prolonging the QT interval or inducing Torsades de Pointes (please refer to http://www.azcert.org/medical-pros/drug-lists/drug-lists.cfm) 2. Strong inhibitors or strong inducers of CYP3A4/5 (please refer to http://medicine.iupui.edu/flockhart/table.htm or http://www.druginteractioninfo.org) 3. Herbal supplements