Resorption and remodelling of skeletal tissues is required for development and growth, mechanical adaptation, repair, and mineral homeostasis of the vertebrate skeleton. Here we review for the first time the current knowledge about resorption and remodelling of the skeleton in teleost fish, the largest and most diverse group of extant vertebrates. Teleost species are increasingly used in aquaculture and as models in biomedical skeletal research. Thus, detailed knowledge is required to establish the differences and similarities between mammalian and teleost skeletal remodelling, and between distantly related species such as zebrafish (Danio rerio) and medaka (Oryzias latipes). The cellular mechanisms of differentiation and activation of osteoclasts and the functions of teleost skeletal remodelling are described. Several characteristics, related to skeletal remodelling, distinguish teleosts from mammals. These characteristics include (a) the absence of osteocytes in most species; (b) the absence of haematopoietic bone marrow tissue; (c) the abundance of small mononucleated osteoclasts performing non-lacunar (smooth) bone resorption, in addition to or instead of multinucleated osteoclasts; and (d) a phosphorus- rather than calcium-driven mineral homeostasis (mainly affecting the postcranial dermal skeleton). Furthermore, (e) skeletal resorption is often absent from particular sites, due to sparse or lacking endochondral ossification. Based on the mode of skeletal remodelling in early ontogeny of all teleosts and in later stages of development of teleosts with acellular bone we suggest a link between acellular bone and the predominance of mononucleated osteoclasts, on the one hand, and cellular bone and multinucleated osteoclasts on the other. The evolutionary origin of skeletal remodelling is discussed and whether mononucleated osteoclasts represent an ancestral type of resorbing cells. Revealing the differentiation and activation of teleost skeletal resorbing cells, in the absence of several factors that trigger mammalian osteoclast differentiation, is a current challenge. Understanding which characters of teleost bone remodelling are derived and which characters are conserved should enhance our understanding of the process in fish and may provide insights into alternative pathways of bone remodelling in mammals.