Abstract: There are classical theorems that all finite dimensional (rational) representations of Lie groups are completely reducible (this includes Maschke's theorem). This fails in positive characteristic. The result obviously fails for p-groups in characteristic p or more generally if the group has a normal p-subgroup (or unipotent subgroup). We will discuss the result that says this is the only reason if the dimension of the representation is small enough. A special case of this result answers a question of Serre about vanishing of the first cohomology group. The critical case in analyzing this is the case of a simple group. We will also discuss results starting from the Landazuri-Seitz results of the 70's to more recent results about small (projective) representations of finite simple groups.