Certain incremental path-independent integrals, of relevance in the mechanics of fracture of elastic-plastic materials described by a classical flow theory of plasticity, are presented. Both quasi-static as well as dynamic fracture situations are considered. The topics discussed include: (i) incremental path-independent integrals that characterize the crack-tip fields in elastic-plastic materials; (ii) incremental integrals related to the incremental total potential energy difference; and (iii) the complementary or dual representations of these integrals. The use of these integrals is illustrated through some numerical examples. Comments are made on the utility of these integrals in postulating rational fracture criteria.