In 1951, Higman introduced the first examples of infinite finitely presented groups with no nontrivial finite quotient. They have a simple presentation, with k\ge 4 generators, where two consecutive generators (considered cyclically) generate a Baumslag-Solitar subgroup BS(1,2). Higman groups have received a lot of attention and remain mysterious in many ways. We study them from the viewpoint of measured group theory, and prove a superrigidity theorem in measure equivalence (a notion introduced by Gromov as a measurable analogue of quasi-isometry), as soon as the number k of generators is at least 5. I will explain the context and motivations, some consequences, and the main ideas from the proof. This is joint work with Jingyin Huang.