We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on some developments that took place within the "Numerical Relativity and High Energy Physics" network, a Marie Curie IRSES action that we coordinated, namely: spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar-tensor gravity, superradiant instabilities and hairy black hole solutions in Einstein's gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog gravity models.