A compact flat Lorentzian manifold is the quotient of the Minkowski space by a discrete subgroup \(\Gamma\) of the isometry group, acting properly, freely and cocompactly on it. A classical result by Goldman, Fried and Kamishima states that, up to finite index, \(\Gamma\) is a uniform lattice in some connected Lie subgroup of the isometry group, acting properly and cocompactly, generalizing Bieberbach theorem to the Lorentzian signature. Such compact quotients are called "standard". More generally, a compact quotient of a homogeneous space \(G/H\) of a Lie group \(G\) is standard if the fundamental group action extends to a proper cocompact action of a connected Lie subgroup of \(G\). It turns out that looking for standard quotients is an easier problem when studying the existence of compact quotients of homogeneous spaces. This talk is about compact locally homogeneous plane waves. Plane waves can be thought of as a deformation of Minkowski spacetime, they are of great mathematical and physical interests. In this talk, we describe the isometry group of a 1-connected homogeneous non-flat plane wave, and show that compact quotients are “essentially" standard. As an application, we obtain that the parallel flow of a compact plane wave is equicontinuous. This is a joint work with M. Hanounah, I. Kath and A. Zeghib.