Three-dimensional bioprinting uses additive manufacturing techniques for the automated fabrication of hierarchically organized living constructs. The building blocks are often hydrogel-based bioinks, which need to be printed into structures with high shape fidelity to the intended computer-aided design. For optimal cell performance, relatively soft and printable inks are preferred, although these undergo significant deformation during the printing process, which may impair shape fidelity. While the concept of good or poor printability seems rather intuitive, its quantitative definition lacks consensus and depends on multiple rheological and chemical parameters of the ink. This review discusses qualitative and quantitative methodologies to evaluate printability of bioinks for extrusion- and lithography-based bioprinting. The physicochemical parameters influencing shape fidelity are discussed, together with their importance in establishing new models, predictive tools and printing methods that are deemed instrumental for the design of next-generation bioinks, and for reproducible comparison of their structural performance.