Phase space crystal is the state of a physical system that displays discrete symmetry in phase space instead of real space. For a single-particle system, the phase space crystal state refers to the eigenstate of the Hamiltonian for a closed quantum system or the eigenoperator of the Liouvillian for an open quantum system. For a many-body system, phase space crystal is the solid-like crystalline state in phase space. The general framework of phase space crystals is to extend the study of solid state physics and condensed matter physics into phase space of dynamical systems. While real space has Euclidean geometry, phase space is embedded with classical symplectic geometry or quantum noncommutative geometry.