The III-V compound semiconductors exhibit superb electronic and optoelectronic properties. Traditionally, closely lattice-matched epitaxial substrates have been required for the growth of high-quality single-crystal III-V thin films and patterned microstructures. To remove this materials constraint, here we introduce a growth mode that enables direct writing of single-crystalline III-V's on amorphous substrates, thus further expanding their utility for various applications. The process utilizes templated liquid-phase crystal growth that results in user-tunable, patterned micro and nanostructures of single-crystalline III-V's of up to tens of micrometres in lateral dimensions. InP is chosen as a model material system owing to its technological importance. The patterned InP single crystals are configured as high-performance transistors and photodetectors directly on amorphous SiO2 growth substrates, with performance matching state-of-the-art epitaxially grown devices. The work presents an important advance towards universal integration of III-V's on application-specific substrates by direct growth.