We report on hybrid organic-inorganic optoelectronic sysbsystems that integrate passive and active optical functions. The integration approaches involve various levels of hybridization, from splicing of pigtailed elements, to chip-to-chip attachment, to hybrid on-chip integration involving grafting and flip-chip mounting, and finally to true heteroepitaxy. The materials integrated include polymer, silica, silicon, silicon oxynitride, lithium niobate, indium phosphide, gallium arsenide, yttrium iron garnet, and neodymium iron boron. The functions enabled by this hybridization approach span the range of functions needed in optical circuitry, while using the highest-performance material system for each element. We demonstrate a number of hybrid subsystems, including fully reconfigurable optical add/drop multiplexers and tunable optical transmitters.