Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy $\{\pm \mathrm{Id}\}$), called flat laminations, and we define transverse measures on flat laminations similar to transverse measures on hyperbolic laminations, taking into account that the images of the leaves of a flat lamination are in...