Fused deposition modeling (FDM) is an additive manufacturing (AM) process that is often used to fabricate geometrically complex shaped prototypes and parts. It is gaining popularity as it reduces cycle time for product development without the need for expensive tools. However, the commercialization of FDM technology in various industrial applications is currently limited due to several shortcomings, such as insufficient mechanical properties, poor surface quality, and low dimensional accuracy. The qualities of FDM-produced products are affected by various process parameters, for example, layer thickness, build orientation, raster width, or print speed. The setting of process parameters and their range depends on the section of FDM machines. Filament materials, nozzle dimensions, and the type of machine determine the range of various parameters. The optimum setting of parameters is deemed to improve the qualities of three-dimensional (3D) printed parts and may reduce post-production work. This paper intensively reviews state-of-the-art literature on the influence of parameters on part qualities and the existing work on process parameter optimization. Additionally, the shortcomings of existing works are identified, challenges and opportunities to work in this field are evaluated, and directions for future research in this field are suggested.