The Margulis Lemma states that in a hyperbolic manifold, the subgroup of the fundamental group generated by small loops around a certain point behaves like an abelian group (more precisely, it is virtually nilpotent). I will present many generalizations of this result that have been appearing in the last 50 years, including recent work (with Qin Deng, Jaime Santos, and Xinrui Zhao) where we include RCD spaces, a non-smooth analogue of manifolds with a lower bound on the Ricci curvature.