  The wide applications of higher dimensional gravity and gauge/gravity duality
have fuelled the search for new stationary solutions of the Einstein equation
(possibly coupled to matter). In this topical review, we explain the
mathematical foundations and give a practical guide for the numerical solution
of gravitational boundary value problems. We present these methods by way of
example: resolving asymptotically flat black rings, singly-spinning lumpy black
holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small
rotating black holes in AdS$_5\times S^5$. We also include several tools and
tricks that have been useful throughout the literature.
