The promise of multicolor (multiple bandgap) solar converters for achieving conversion efficiencies in excess of 25% in space or 30% in terrestrial applications has been widely discussed. We describe current results of efforts to reach these performance goals with two cell monolithic stacks containing an intercell ohmic contact. Basic requirements for the successful fabrication of high efficiency tandem structures are defined, and the apparent practical limitations on the formation of such multiple bandgap solar cells by presently available techniques are identified. Experimental tandem or "cascaded" structures made by M0-CVD, LPE and MBE growth techniques in various materials combinations are described and current performance results are presented.