First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic geometry which allows for the study of Hamiltonian dynamics on a wider range of manifolds while preserving the local properties of symplectic geometry. After a long period of hibernation (especially as far as the topological aspect is concerned), interest in this subject has picked up again recently. However, to this day, the field of LCS topology remains vastly unexplored.In this talk, we will introduce the various objects of LCS geometry and their behavior through both definitions and examples. We will also explore some questions around an LCS version of the nearby Lagrangian conjecture and some of the connections between LCS and contact geometry.