This article aims to understand the rheology of collagen networks and their role in various stages of a bioprinting process while building tissue-like constructs. The science of rheology, which deals with the deformation and flow of matter, has grown considerably from its earlier focus on polymer melts and solutions and their processing methods to hydrogels with new processing procedures, such as bioprinting. The main objective of this paper is to discuss the impact of the rheology of collagen hydrogels on micro-extrusio and layer stacking stages of bioprinting. Generally, the rheological characterization of hydrogels, including collagens by dynamic measurements under small deformations, is considered sufficient to evaluate their bioprinting performance. However, we brought out the importance of other rheological properties of collagen networks such as steady-state shear flow conditions and large amplitude oscillator shear. While the dynamic measurements under small deformations are useful for characterizing the crosslinking and gel formations of the collagen, the steady shear flow measurements are better tools for investigating filament micro-extrusion and layer-stacking stages of a bioprinting process. We brought the role of other non-Newtonian material functions, such as first normal stress difference and extensional viscosity in addition to shear viscosity, for the first time. Extensional viscosity and the viscoelasticity manifested through normal-stress differences are significant in capillary (needle) flow. We also suggested caution to use of dynamic viscosity vs. oscillation frequency under small deformations in the place of steady shear viscosity vs. shear rate measurement. In addition, we brought out the importance of the large amplitude oscillatory shear test to investigate the collagen networks under large deformations. Finally, we discussed the role of crosslinking and flow conditions on cell viability. Those discussions are focused on collagen networks; nevertheless, they are valid on the bioprinting of other hydrogels.