pp-waves are the simplest (and the first obtained) non-linear radiative solution in general relativity. The realization of memory effects induced by vacuum gravitational plane wave (VGPW) (a specific subset of pp-waves) on a couple of test particles has been extensively study (https://arxiv.org/abs/1704.05997, https://arxiv.org/abs/1705.01378, https://arxiv.org/abs/1803.09640). So far, the work has focused on the velocity memory effect and until recently, it was believed that no displacement memory could be realized in such radiative geometry. In this talk, I will show that both displacement and velocity memories can be induced by a VGPW and I will present the first general classification for the conditions under which this happens. This classification holds for both pulse and step profiles (the latter case being the standard ad hoc model for implementing memory contribution to the waveform profile. See https://arxiv.org/abs/1108.3121) and allows to understand the numerical examples presented recently in https://arxiv.org/abs/2405.12928. Along the way, I will review several key results to analyze the geodesic motion and geodesic deviation equation in VGPW, and in particular the explicit and hidden symmetries of these geometries. I will further show that polarized VGPW enjoys a new type of symmetry under Möbius reparametrization of the null time (which turns out to be a more general property inherent to any null hypersurface). I will also review some theorems relating hidden symmetries (under Killing tensors) and the solution space of the geodesic deviation equation used to identify the memory effects. This talk is based on the recent article: https://inspirehep.net/literature/2796995
