In this talk I will discuss recent development related to some exactly solvable lower-dimensional gravity models. After a broader motivation of this field, the main focus will be the interrelation between three a priori very distinct models: the JT gravity model, Liouville gravity, and the double-scaled SYK model. Their amplitudes in particular can be formulated in a very similar group-theoretical language. An explanation for this fact can be found when describing all three of them in terms of dilaton gravity models with different dilaton potentials.
