Bioprinting allows to spatially organize cellular niches influencing mechanobiology into tissue engineered constructs thereby aiming to achieve a similar functional complexity as the various tissues present within bone. Natural polymer hydrogel matrices are favorably selected as part of many bioinks thanks to their level of mimicry with the bone osteoid matrix. More specifically, a variety of biophysical and biochemical cues targeting osteogenesis can be presented towards cells encapsulated in bioprinted constructs. This review focusses on delineating bioprinting targeting osteogenesis based on the printing approach (deposition-versus light-based bioprinting) and crosslinking chemistry utilized (chain- versus step-growth crosslinking). Moreover, the cell-biomaterial interactions at play within these constructs are addressed in line with currently established mechanobiology concepts. The delicate interplay between the presented cues from the encapsulating matrix, the used printing process and the maturity, source and concentration of the used cell type finally dictates the osteoregenerative outcome of a bioprinted construct. Given the advantages towards cell encapsulation associated with step-growth systems, there is a huge need to evaluate these systems in comparison to the heavily reported chain-growth systems (predominantly gelatin-methacryloyl or GelMA) towards the bioprinting of constructs serving osteogenesis. Moreover, multiple bioprinting strategies should be combined to tackle key challenges in the field and enable functional and scalable hierarchical constructs serving osteogenesis with incorporation of vascularization and innervation.