To assist the transition of 3D bioprinting technology from simple lab-based tissue fabrication, to fully functional and implantable organs, the technology must not only provide shape control, but also functional control. This can be accomplished by replicating the cellular composition of the native tissue at the microscale, such that cell types interact to provide the desired function. There is therefore a need for precise, controllable, multi-material printing that could allow for high, possibly even single cell, resolution. This paper aims to draw attention to technological advancements made in 3D bioprinting that target the lack of multi-material, and/or multi cell-type, printing capabilities of most current devices. Unlike other reviews in the field, which largely focus on variations in single-material 3D bioprinting involving the standard methods of extrusion-based, droplet-based, laser-based, or stereolithographic methods; this review concentrates on sophisticated multi-material 3D bioprinting using multi-cartridge printheads, co-axial nozzles and microfluidic-enhanced printing nozzles.