Given a generically d-rigid graph on n vertices, how many lacations for the vertices suffice to rigidify it in d-space? Likewise for infinite families of such graphs, e.g. all planar Laman graphs, all triangulations of a given surface, all triangulated surfaces, all n-vertex d-rigid graphs etc. I'll focus on families where the answer is a constant (independent on n), surveying results by Fekete and Jordan, Adiprasito and me, Kiraly, and recent ones with my former student Simion Tarabykin.