Finite simple groups of low rank: Hurwitz generation and (2,3)-generation

Let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree ≤ 7 over an algebraically closed field F of characteristic p ≥ 0. We survey some recent results which lead to the complete list of the groups in this set which are (2,3,7)-generated and of those which are (2,3)-generated