Spacetimes, like Minkowski space, are omnipresent in physics. We will review a classification of spacetimes that generalizes the classification of maximally symmetric lorentzian geometries and includes further physically interesting ones. Based on these spacetimes we will discuss limits and extensions of three-dimensional gravity and two-dimensional Jackiw-Teitelboim gravity. Special focus will be given to the underlying algebraic structure and gauge theoretic Chern-Simons and BF formulations.