Let G be a finite group and let P=P1, …; Pm be a sequence of Sylow pi -subgroups of G, where p1;…; pm are the distinct prime divisors of |G|. The Sylow multiplicity of g 2 G in P is the number of distinct factorizations g=g1 … gm such that gi Î Pi. We review properties of the solvable radical and the solvable residual of G which are formulated in terms of Sylow multiplicities, and discuss some related open questions.