The center of the Galaxy is one of the prime targets in the search for a signal of annihilating (or decaying) dark matter. If such a signal were to be detected, it would shed light on one of the biggest mysteries in physics today: What is dark matter? Fundamental properties of the particle nature of dark matter, such as its mass, annihilation cross section, and annihilation final states, could be measured for the first time. Several experiments have searched for such a signal, and some have measured excesses that are compatible with it. A long-standing and compelling excess is observed in γ-rays by the Fermi Large Area Telescope ( Fermi–LAT). This excess is consistent with a dark matter particle with a mass of approximately 50 (up to ∼200) GeV annihilating with a velocity-averaged cross section of ∼10−26 cm3 s−1. Although a dark matter origin of the excess remains viable, other interpretations are possible. In particular, there is some evidence that the excess is produced by a population of unresolved point sources of γ-rays—for example, millisecond pulsars. In this article, I review the current status of the observation of the Fermi–LAT Galactic center excess, the possible interpretations of the excess, the evidence and counterevidence for each, and the prospects for resolving its origin with future measurements.