Microfluidic technologies are emerging as an enabling tool for various applications in tissue engineering and cell biology. One emerging use of microfluidic systems is the generation of shape-controlled hydrogels (i.e., microfibers, microparticles, and hydrogel building blocks) for various biological applications. Furthermore, the microfluidic fabrication of cell-laden hydrogels is of great benefit for creating artificial scaffolds. In this paper, we review the current development of microfluidic-based fabrication techniques for the creation of fibers, particles, and cell-laden hydrogels. We also highlight their emerging applications in tissue engineering and regenerative medicine.