One of the most common types of 3D printing technologies is inkjet printing due to its numerous advantages, including low cost, programmability, high resolution, throughput, and speed. Inkjet printers are also capable of fabricating artificial tissues with physiological characteristics similar to those of living tissues. These artificial tissues are used for disease modeling, drug discovery, drug screening, and replacements for diseased or damaged tissues. This paper reviews recent advancements in one of the most common 3D printing technologies, inkjet dispensing. We briefly consider common printing techniques, including fused deposition modeling (FDM), stereolithography (STL), and inkjet printing. We briefly discuss various steps in inkjet printing, including droplet generation, droplet ejection, interaction of droplets on substrates, drying, and solidification. We also discuss various parameters that affect the printing process, including ink properties (e.g., viscosity and surface tension), physical parameters (e.g., internal diameter of printheads), and actuation mechanisms (e.g., piezoelectric actuation and thermal actuation). Through better understanding of common 3D printing technologies and the parameters that influence the printing processes, new types of artificial tissues, disease models, and structures for drug discovery and drug screening may be prepared. This review considers future directions in inkjet printing research that are focused on enhancing the resolution, printability, and uniformity of printed structures.