Indium phosphide (InP) nanowires and nanotubes have been synthesized via the vapor-liquid-solid (VLS) growth mechanism. The wires as well as the tubes are crystalline and have the (bulk) zinc blende structure. Compared to the nanowires the nantubes are formed at higher temperatures. A simple model for the formation of the nanotubes is presented. The diameter of the wires and the wall thickness of the tubes can be controlled by the synthesis temperature. Photoluminescence measurements on individual wires show a strong polarization dependency. Moreover, the nanostructures exhibit a considerable blue shift with respect to bulk emission as a result of size-quantization. In addition, this blue shift indicates that the optical properties are not dominated by defect states.