The fabrication of human tissues and organs exhibiting structural, mechanical and biological function remains a major challenge due to their structural complexity, multicellular composition, spatial heterogeneity of the ECM and, in most cases, the presence of a vascular network. The unique ability of bioprinting technologies to deposit cells, biomaterials and bioactive molecules into precise locations in 3D has provided new opportunities in the fabrication of grafts for tissue repair and in vitro models with high degree of accuracy, automation and reproducibility. The success of bioprinting is intimately linked to the design of biomimetic materials as they aim to recapitulate the ECM properties and support essential cellular functions, such as adhesion, migration, proliferation and de novo tissue synthesis. This talk will discuss the rational design of biomaterials for 3D bioprinting, providing examples of strategies that can be used to control the printability and shape fidelity of 3D hydrogels. The regulatory role of biophysical and biochemical properties of biomaterials on cell response will be also discussed, along with key research findings demonstrating the importance of mechanical properties of the cell microenvironment on the biological function of bioprinted constructs.