Bioprinting offers tremendous potential in the fabrication of functional tissue constructs for replacement of damaged or diseased tissues. Among other fabrication methods used in tissue engineering, bioprinting provides accurate control over the construct's geometric and compositional attributes using an automated approach. Bioinks are composed of the hydrogel material and living cells that are critical process variables in the fabrication of functional, mechanically robust constructs. Appropriate cells can be encapsulated in bioinks to create functional tissue structures. Ideal bioinks are required to undergo a sol–gel transition consuming minimal processing time, and a plethora of chemical and physical crosslinking mechanisms are generally exploited to achieve high shape fidelity and construct stability. In contrast, crosslinking of hydrogel material at rapid rates can cause nozzle clogging, and hence, optimization of the bioink is often necessary. Bioinks can be formulated using natural or synthetic biomaterials, alone or in combination of these biomaterials. Herein, the various bioprinting methods are discussed; the natural, synthetic, or hybrid materials used as bioinks are analyzed; and the challenges, limitations, and future directions concerning the bioprinting technique are appraised.