let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $mathbb{f}$ of characteristic $pgeq 0$. 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.
