Extrusion bioprinting has exciting prospects in fabricating organized tissue constructs by simultaneous dispensing of cells and matrix materials to repair or replace damaged or diseased tissues and organs. The exhilarating capability of this technique is to generate constructs with spatial variations of cells along multiple axes with high geometric complexity. A variety of bioprinters based on extrusion principle have been developed around the world and many are even commercialized. These computer-controlled technologies to design and fabricate tissues will enhance our understanding of the governing factors of tissue formation and function. Moreover, it will provide a valuable tool for several emerging technologies including tissue engineering. In this chapter, we discuss the rationale of extrusion-based bioprinting for fabrication of tissue constructs. Current strategies of building tissue constructs are discussed; in particular, their merits and demerits and the requirements to move the current concepts to practical application are highlighted. © 2015 Elsevier Inc. All rights reserved.