Many intrinsically disordered proteins self-assemble into liquid droplets that function as membraneless organelles. Because of their biological importance and ability to colocalize molecules at high concentrations, these protein compartments represent a compelling target for bio-inspired materials engineering. Here we manipulated the intrinsically disordered, arginine/glycine-rich RGG domain from the P granule protein LAF-1 to generate synthetic membraneless organelles with controllable phase separation and cargo recruitment. First, we demonstrate enzymatically triggered droplet assembly and disassembly, whereby miscibility and RGG domain valency are tuned by protease activity. Second, we control droplet composition by selectively recruiting cargo molecules via protein interaction motifs. We then demonstrate protease-triggered controlled release of cargo. Droplet assembly and cargo recruitment are robust, occurring in cytoplasmic extracts and in living mammalian cells. This versatile system, which generates dynamic membraneless organelles with programmable phase behavior and composition, has important applications for compartmentalizing collections of proteins in engineered cells and protocells.