Let $m$ and $h$ be a measured lamination and a hyperbolic metric on a closed surface $S$. The image of $h$ by the right earthquake along $m$ is obtained (at least in simple cases) by "cutting" $S$ open along $m$, sliding the right-hand side, and gluing back. Thurston's Earthquake Theorem asserts that there is a unique right earthquake connecting any two hyperbolic metrics. We will explain (following G. Mess) the deep relations between this theorem and the geometry of 3-dimensional AdS manifolds. Considering physically relevant 3-manifolds ——containing "particles", or multi-black holes—— leads to extensions of Thurston's theorem to hyperbolic surfaces with cone singularities or with geodesic boundary. (Part of the results were obtained with F. Bonsante and/or K. Krasnov).