In this talk we study the cover time, i.e. the duration to visit every site of a finite graph. In 2012, Ding et al. published an inspiring result that the asymptotics of the cover time can be estimated by the maximum of the corresponding discrete gaussian free field for general graphs, and since then people have begun looking for sharper results, starting with trees. I will present these ideas (local time, Ray-Knight theorem, extremal landscape) leading to sharp estimates of the cover time for trees.