Surface roughness is gaining increasing recognition in the processing design methods of additive manufacturing (AM) due to its role in many critical applications. This impact extends not only to various AM product manufacturing but also to indirect applications, such as molding and casting. This review article discusses the role of processing on the surface roughness of AM-printed polymers with limited post-processing by summarizing recent advances. This review offers a benchmark for surface quality improvement of AM processes, considering the surface roughness of polymeric parts. For this purpose, it lists and analyzes the key processes and various printing parameters used to monitor and adjust surface roughness under given constraints. Four AM techniques for manufacturing polymeric parts are compared: fused filament fabrication (FFF), selective laser sintering (SLS), vat photopolymerization (VPP), and material jetting (MJT). A review and discussion of recent studies are presented, along with the most critical process parameters that affect surface roughness for the selected AM techniques. To assist in selecting the most appropriate method of 3D printing, comparable research summaries are presented. The outcome is a detailed survey of current techniques, process parameters, roughness ranges, and their applicability in achieving surface quality improvement in as-printed polymers.