There is an exact mapping between Liouville theory with c ≥ ≥ 25 , and certain log-correlated random energy models. These models describe a thermal particle in a random potential that is logarithmically correlated. In two dimensions, such potential coincides with the Gaussian free field. In that case, certain correlation functions between primary fields in the Liouville theory are mapped to correlation functions of the Gibbs measure of the particle. This has applications to extreme value statistics of the two-dimensional Gaussian free field, and allows to predict certain universal properties of the log-correlated random energy models (in two dimensions and beyond).