Nowadays, it is possible to produce products with complex geometries, thanks to the experts who have continuously explored the advancements in additive manufacturing (AM) techniques. This review helps readers understand the opportunities and difficulties associated with developing parts for various industries, including aerospace, tooling, electronics, and biomedicine. The present work describes the landscape of polymeric composites using laminated object manufacturing (LOM) and fused deposition modeling (FDM). This paper discusses recent publications in the realm of AM related to composite fabrication, materials, techniques, functionality, and future scope. The effects of nanofiller reinforcement on the mechanical properties of composites have been thoroughly investigated. Furthermore, FDM process parameters such as layer thickness, infill speed, nozzle temperature, and raster angle have also been considered. Finally, the challenges and potential applications of LOM and FDM of additively manufactured composites have been summarized.