The remarkable performance of lead halide perovskites in solar cells can be attributed to the excellent photophysical properties that are also ideal for lasers and light-emitting devices (LEDs). Here we first report new insights on the crystal growth of the perovskite materials and developed the solution growth of single crystal nanowires, nanorods, and nanoplates of methylammonium (MA), formamidinium (FA) and all-inorganic cesium (Cs) lead halides perovskites (APbX3) via a dissolution-recrystallization pathway. We also developed the vapor phase epitaxial growth of CsPbX3 perovskite nanowires and single-crystal thin films. Moreover, chemical strategies to stabilize the nanostructures of metastable perovskite phases, such as FAPbI3 and CsPbI3, have been developed by using surface ligands. We demonstrated high performance room temperature lasing with broad tunability of emission color from 420 nm to 824 nm from single-crystal lead halide perovskite nanowires with estimated lasing quantum yields approaching 100%. LEDs can also be fabricated with nanoscale structures of 3D or 2D perovskites. The excellent properties of these single-crystal perovskite nanostructures of diverse families of perovskite materials with different cations, anions, and dimensionality make them ideal for fundamental physical studies of carrier transport and decay mechanisms, and for enabling high performance semiconductor lasers, LEDs, and other optoelectronic applications.