The exciting intrinsic properties discovered in single crystals of metal halide perovskites still await their translation into optoelectronic devices. The poor understanding and control of the crystallization process of these materials are current bottlenecks retarding the shift towards single crystal-based optoelectronics. Here we theoretically and experimentally elucidate the role of surface tension in the rapid synthesis of perovskite single crystals by inverse temperature crystallization (ITC). Understanding the nucleation and growth mechanisms enabled us to exploit surface tension to direct the growth of monocrystalline films of perovskites (AMX3, where A = CH3NH3+ or MA; M = Pb2+, Sn2+; X = Br-, I-) on the solution surface. We achieve up to 1 cm2-sized monocrystalline films with thickness on the order of the charge carrier diffusion length (~5-10 µm). Our work paves the way to control the crystallization process of perovskites, including thin film deposition, which is essential to advance the performance benchmarks of perovskite optoelectronics.