  The demand to obtain answers to highly complex problems within strong-field
gravity has been met with significant progress in the numerical solution of
Einstein's equations - along with some spectacular results - in various setups.
We review techniques for solving Einstein's equations in generic spacetimes,
focusing on fully nonlinear evolutions but also on how to benchmark those
results with perturbative approaches. The results address problems in
high-energy physics, holography, mathematical physics, fundamental physics,
astrophysics and cosmology.
