Relapsed/refractory Multiple Myeloma (MM) is an incurable disorder with a poor prognosis. Carfilzomib is a novel proteasome inhibitor with activity in this setting. Panobinostat is a pan-deacetylase inhibitor which has shown synergistic cytotoxicity in vitro and in vivo with proteasome inhibitors. The combination should enhance the activity of both agents against myeloma cells. In Phase I, the optimal doses of the combination of carfilzomib and panobinostat will be determined. Assuming this combination is feasible, the Phase II portion will proceed using the doses determined in Phase I.