Metal halide semiconductors with perovskite crystal structures have recently emerged as highly promising optoelectronic materials. Despite the recent surge of reports on microcrystalline, thin-film and bulk single-crystalline metal halides, very little is known about the photophysics of metal halides in the form of uniform, size-tunable nanocrystals. Here we report low-threshold amplified spontaneous emission and lasing from ∼10 nm monodisperse colloidal nanocrystals of caesium lead halide perovskites CsPbX3 (X=Cl, Br or I, or mixed Cl/Br and Br/I systems). We find that room-temperature optical amplification can be obtained in the entire visible spectral range (440-700 nm) with low pump thresholds down to 5±1 μJ cm(-2) and high values of modal net gain of at least 450±30 cm(-1). Two kinds of lasing modes are successfully observed: whispering-gallery-mode lasing using silica microspheres as high-finesse resonators, conformally coated with CsPbX3 nanocrystals and random lasing in films of CsPbX3 nanocrystals.