  Throughout the Universe many powerful events are driven by strong
gravitational effects that require general relativity to fully describe them.
These include compact binary mergers, black hole accretion and stellar
collapse, where velocities can approach the speed of light, and extreme
gravitational fields --$\Phi_{\rm Newt}/c^2 \simeq 1$-- mediate the
interactions. Many of these processes trigger emission across a broad range of
the electromagnetic spectrum. Compact binaries further source strong
gravitational wave emission that could directly be detected in the near future.
This feat will open up a gravitational wave window into our Universe and
revolutionize its understanding. Describing these phenomena requires general
relativity, and --where dynamical effects strongly modify gravitational
fields-- the full Einstein equations coupled to matter sources. Numerical
relativity is a field within general relativity concerned with studying such
scenarios that cannot be accurately modeled via perturbative or analytical
calculations. In this review, we examine results obtained within this
discipline, with a focus on its impact in astrophysics.
