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Biofabrication is the cutting-edge process of additively manufacturing complex living tissues and scaffolds, representing a game-changing progression for the field of regenerative medicine. Complementary to traditional tissue engineering, biofabrication offers exceptional precision and control over the spatial distribution of cells and materials. With rapid advancements in biofabrication, innovative bioprinting and bioassembly techniques have emerged, converging with classic manufacturing processes to construct an extensive suite of hybrid fabrication methods. However, the role of physics in biofabrication is often overlooked. To further propel research in this field, it is imperative that the fundamental biophysical and rheological prerequisites are characterised and accounted for during the development of novel bioink formulations and biofabrication lines. This themed Collection addresses the above-described issue by inviting original research that describes the latest advances in understanding the biophysical parameters that dictate the bioink rheology and cross-linking. We also welcome studies that exploit this fundamental understanding to enable the production of complex tissues as well as the modulation of cell function and cell-material interactions.