It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutelyp-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable stronglyp-summing multilinear operators, (p1, . . . , pn)-dominated multilinear operators and dominated (p1, . . . , pn;σ)-continuous multilinear operators. [ABSTRACT FROM PUBLISHER]