This is an open label phase I trial designed to evaluate the maximum tolerated dose, dose-limiting toxicities, pharmacokinetics, and activity of the combination of alsertib (MLN8237) and brentuximab vedotin in patients with relapsed/refractory CD30-positive lymphomas and solid malignancies. Cohorts of 3-6 patients will receive escalating or de-escalating doses of MLN8237 based on a 3 + 3 design.