Microassembly promises to extend MEMS beyond the confines of silicon micromachining. This paper surveys research in both serial and parallel microassembly. The former extends conventional `pick and place' assembly into the micro- domain, where surface forces play a dominant role. Parallel assembly involves the simultaneous precise organization of an ensemble of micro components. This can be achieved by microstructure transfer between aligned wafers or arrays of binding sites that trap an initially random collection of parts. Binding sites can be micromachined cavities or electrostatic traps; short-range attractive forces and random agitation of the parts serve to fill the sites. Microassembly strategies should furnish reliable mechanical bonds and electrical interconnection between the micropart and the target substrate or subassembly.