Although fish species represent probably about half of all vertebrate species, the structure and material properties of fish skeletons are poorly understood. Since osteocytes (cells within the bone tissue) are believed to orchestrate the modeling and remodeling responses in mammalian bone, the unique lack of these cells in the bones of the majority of extant fishes (neoteleosts), raises several intriguing questions. In particular, how do their bones handle forces, especially those applied repeatedly and over long periods of time. This paper reviews the available information regarding the structure-function relationship of teleost bones – namely their known structural features, mechanical properties and response to load – with a particular focus on the acellular bone of neoteleosts. We present preliminary results of ongoing investigations in these areas and highlight topics (e.g. mechanisms of tissue fatigue, repair and resistance to high strain rates) we believe particularly ripe for and demanding further investigation.