Ultralight dark matter refers to the lightest potential dark matter candidates. We will focus on the mass range that has been studied using gravitational signatures on astrophysical and cosmological observations, corresponding to a mass ${10}^{-24}eV\lesssim m\lesssim {10}^{-18}eV$. We will discuss the motivations for this mass range. The most studied model in this range corresponds to a minimally coupled, single, classical, spin-0 field comprising all dark matter, originally proposed as ``fuzzy" dark matter. However, the work exploring extensions of this model (for example, higher spin, self-coupled, multiple field, and mixed models) will be one of the focuses of this review. The phenomenology associated with ultralight dark matter is rich and includes linear effects on the linear power spectrum, solitonic core structures forming at the center of halos, nonlinear effects resulting in heating of stellar distributions, and relativistic effects relating to pulsar signals and black hole superradiance, to name a few. This set of effects has been studied using an equally extensive set of numerical tools. We will summarize the most common ones and discuss their applications and limitations. Ultralight dark matter also has a wide variety of observational constraints, including those from halo mass functions, the Lyman-alpha forest, halo density profiles, stellar dynamics, and black hole spins. We will review them, focusing on the observations made, the method of study, and the major systematics. We will end with a discussion of the status of the field and future work needed.