Spacetimes, like Minkowski space, are omnipresent in physics. I will introduce a recent classification of spacetimes that generalizes the classification of maximally symmetric lorentzian geometries and includes further physically interesting ones. Among them are galilean, carrollian and aristotelian geometries for which there is renewed interest due to applications in holography. These spacetimes posses infinite dimensional (BMS-like) symmetries which we will discuss. Finally, I will explain how gravitational theories based on these spacetimes can be constructed.

Based on: arXiv:1809.01224, arXiv:1903.09165, arXiv:1905.00034,
(arXiv:1612.02277, arXiv:1710.11110)