Brentuximab Vedotin and Bendamustine for the Treatment of Hodgkin Lymphoma and Anaplastic Large Cell Lymphoma (ALCL)

Inclusion Criteria: * Histologically confirmed relapsed or refractory HL or ALCL. * Documented CD30+ expression from either original diagnosis or a tumor biopsy in the relapsed setting. * For patients with HL, subjects are eligible after failure or having declined autologous stem cell transplant or at least two prior multi-agent chemotherapy regimens if they are not autologous stem cell transplant candidates. For patients with ALCL, subjects are eligible after failure of at least one prior multi-agent chemotherapy regimen and if they are not eligible for or have declined autologous stem cell transplant. * Must have received first line chemotherapy. No upper limit for the number of prior therapies. * Patients with prior autologous or allogeneic stem cell transplant are eligible as long as they meet all other criteria. * Measurable or evaluable disease, as defined in 2008 Revised Response Criteria for Malignant Lymphoma(33) * Age \> or = 18 years * ECOG performance status 0,1 or 2 * Patient's must have adequate organ and marrow function as defined below * Absolute neutrophil count \> or = 1,000 (1.0 x 109/L) * Platelets \> or = 50,000 (50 x 109/L) * Total Bilirubin \< or = 1.5 x institutional limits unless documented Gilbert's syndrome (then \< 2.5 x institutional upper limit) * AST (SGOT)/ALT (SGPT) \< or = 2.0 x institutional upper limit of normal (unless known hepatic involvement then \< 3.5 x institutional upper limit) * Creatinine within normal institutional limits OR creatinine clearance \> or = 50mL/min for patients with creatinine levels above institutional normal * If female of childbearing age, negative serum pregnancy test within 7 days prior to the first dose of brentuximab vedotin in this study * Must be willing to use contraception during the study, and for 30 days following the last dose of study drug. * Able to understand and to sign a written consent document Exclusion Criteria: * Prior treatment with brentuximab vedotin and bendamustine in combination. May have received prior therapy with brentuximab vedotin or bendamustine separately. * Received either brentuximab vedotin or bendamustine within 3 months of receiving their first dose of protocol based therapy. * If brentuximab vedotin or bendamustine was previously received, had disease progression during the first 3 cycles of either brentuximab vedotin or bendamustine. * Systemic steroids that have not been stabilized to the equivalent of \< 10 mg/day of prednisone 7 days prior to the initiation of the trial. * ANY concurrent investigational agents. * Exposure to chemotherapy, radiotherapy, biologics or investigational agents within 3 weeks prior enrollment in the study. * Known cerebral or meningeal disease. * Active concurrent malignancy (except non-melanoma skin cancer or carcinoma in situ of the cervix). If there is a history of prior malignancy the patients must be disease free and off treatment for \> or = 3 years. * Uncontrolled intercurrent illness including but not limited to: ongoing or active infection, systemic congestive heart failure Class III or IV by NYHA criteria, unstable angina pectoris, or cardiac arrhythmia, or in patients status post allogeneic transplantation with uncontrolled graft versus host disease (GVHD). * Pre-existing neuropathy grade III or greater. * Pregnant or nursing. * Known hypersensitivity to brentuximab vedotin, bendamustine, or mannitol. * Known Human Immunodeficiency Virus (HIV) positive, or hepatitis A, hepatitis B or hepatitis C; if hepatitis Bsurface antigen positive or Bcore antibody positive must have normal liver function tests and be willing and able to take anti-hepatitis medication such as lamivudine or equivalent.