A group G is said to be sharply 2-transitive if it acts on a set X containing at least two elements in such a way that any pair of distinct elements of X can be mapped to any other such pair by a unique element of G. A typical example is the affine group GA(K) for its natural action on the field K. The first examples of sharply 2-transitive groups other than GA(K) were constructed a few years ago by Rips, Segev and Tent. In my talk, I will describe a construction of infinite finitely generated simple sharply 2-transitive groups. Based on works with Katrin Tent and Vincent Guirardel.