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Bioprinters are being extensively used for different applications in life sciences and medicine in general and more specifically in regenerative medicine, tissue, and organ fabrication. The technology has matured from its purely academic origin owing to the involvement of materials science, engineering, biology, and physics, as well as commercial entities. Nevertheless, despite the progress in the science and the understanding of the mechanisms underlying the various bioprinting technologies, further efforts are needed to develop more quantitative strategies. In particular, predictive modeling is necessary to optimize the printing parameters and thus enhance the quality of the final products. Here, we review the physics that underpins the most commonly employed approaches, such as extrusion, laser-based, and inkjet bioprinting. We provide an overview of the relevant parameters, their inter-relationships, and the equations that govern the various printing processes and thus allow for their optimization. We present our perspective on the field and views on future strategies for its further advancement. Our intention with this review is to provide the practitioners of bioprinting with additional tools to enhance the quantitative aspects of their work and move the technology beyond its early, mostly "trial and error" character. [ABSTRACT FROM AUTHOR]