Nowadays, 3D bioprinting technologies are rapidly emerging in the field of tissue engineering and regenerative medicine as effective tools enabling the fabrication of advanced tissue constructs that can recapitulate in vitro organ/tissue functions. Selecting the best strategy for bioink deposition is often challenging and time consuming process, as bioink properties-in the first instance, rheological and gelation-strongly influence the suitable paradigms for its deposition. In this short review, we critically discuss one of the available approaches used for bioprinting-namely co-axial wet-spinning extrusion. Such a deposition system, in fact, demonstrated to be promising in terms of printing resolution, shape fidelity and versatility when compared to other methods. An overview of the performances of co-axial technology in the deposition of cellularized hydrogel fibres is discussed, highlighting its main features. Furthermore, we show how this approach allows (i) to decouple the printing accuracy from bioink rheological behaviour-thus notably simplifying the development of new bioinks-and (ii) to build heterogeneous multi-materials and/or multicellular constructs that can better mimic the native tissues when combined with microfluidic systems. Finally, the ongoing challenges and the future perspectives for the ultimate fabrication of functional constructs for advanced research studies are highlighted.