We present Phantom, a fast, parallel, modular, and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary, and high energy astrophysics, and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, dust–gas mixtures, H2 chemistry, physical viscosity, external forces including numerous galactic potentials, Lense–Thirring precession, Poynting–Robertson drag, and stochastic turbulent driving. Phantom is hereby made publicly available.