The crystallization of amorphous solids impacts fields ranging from inorganic crystal growth to biophysics. Promoting or inhibiting nanoscale epitaxial crystallization and selecting its final products underpins applications in cryopreservation, semiconductor devices, oxide electronics, quantum electronics, structural and functional ceramics, and advanced glasses. As precursors for crystallization, amorphous solids are distinguished from liquids and gases by the comparatively long relaxation times for perturbations of the mechanical stress and for variations in composition or bonding. These factors allow experimentally controllable parameters to influence crystallization processes and to drive materials towards specific outcomes. For example, amorphous precursors can be employed to form crystalline phases, such as polymorphs of Al2O3, VO2, and other complex oxides, that are not readily accessible via crystallization from a liquid or through vapor-phase epitaxy. Crystallization of amorphous solids can further be guided to produce a desired polymorph, nanoscale shape, microstructure, and orientation of the resulting crystals. These effects can enable advances in applications in electronics, magnetic devices, optics, and catalysis. Directions for the future development of the chemical physics of crystallization from amorphous solids can be drawn from the impact of structurally complex and non-equilibrium atomic arrangements in liquids and the atomic-scale structure of liquid-solid interfaces.