With the hundreds of merging binary black holes (BHs) expected to be detected by LIGO, LISA, and other upcoming instruments, the modelling of astrophysical channels that lead to the formation of compact BH binaries has become of crucial importance. BHs of any size can form bound systems in every astrophysical environment, from the field to galactic nuclei. If a binary is too wide, it needs a catalysis process to harden and merge, as in the case a third objects orbiting the BH binary on a distant orbit. In this case, Kozai-Lidov cycles can pump up the binary eccentricity, thus driving it to a merger thanks to efficient energy dissipation at the pericenter. Some remarkable scenarios where the Kozai-Lidov mechanism operates are in triple and quadruple systems of stellar BHs, and in intermediate-mass BH-stellar BH binaries in orbit around a central supermassive BH in galactic nuclei.