Until recently, the existence of non-split sharply 2-transitive groups (i.e., sharply 2-transitive groups without a normal abelian subgroup) was an open problem. The first examples of such groups were exhibited by Rips, Segev and Tent in 2017 and by Rips and Tent in 2019. It is possible to associate to every sharply 2-transitive group a characteristic that is either 0 or a positive prime number. The first of these examples were in characteristic 2, while the others were in characteristic 0, leaving the problem open for odd characteristics. In this talk, I will outline recent progress made in adapting the construction in characteristic 0 to build examples of non-split sharply 2-transitive groups in odd characteristic using methods of geometric small cancellation. I will also give a rough explanation of how these methods relate to the usual small cancellation conditions for group presentations. This is joint work with Simon André and Katrin Tent.