Sponges (phylum Porifera) are an early-branching lineage of Metazoa. The long independent evolution of sponges makes them an essential group for comparative studies of the emergence and early evolution of various aspects of metazoan biology, including asexual reproduction. This review provides a current critical overview of the modes of asexual reproduction in sponges with an emphasis on the morphogeneses accompanying it. Asexual reproduction occurs in all poriferan clades and has three modes: fragmentation, budding, and gemmulation. Fragmentation seems to be a universal, but unspecialized and passive form of asexual reproduction; it relies on the pronounced regeneration capabilities of sponges. Budding and gemmulation are processes that are triggered by endogenous factors and are an integral part of the life cycle in many species. Budding seems to occur in all poriferan classes but differs in its mechanisms between classes: buds in Demospongiae are formed through mesenchymal morphogeneses, while in Homoscleromorpha and Calcarea—through epithelial ones. In contrast to other modes of asexual reproduction, gemmulation is restricted to freshwater demosponges and a few brackish-water marine demosponges. Gemmules represent compact groups of dormant cells, thesocytes, coated by a thick protective coat; in favorable conditions, these cells give rise to a new individual. Gemmulation represents not only a reproduction mechanism but also a mechanism for enduring adverse environmental conditions becoming a very important alternative reproduction strategy for sponges living in discontinuous-fragmented and/or unstable environments.