The worldwide demand for additive manufacturing (AM) is increasing due to its ability to produce more challenging customized objects based on the process parameters for engineering applications. The processing of conventional materials by AM processes is a critically demanded research stream, which has generated a path-breaking scenario in the rapid manufacturing and upcycling of plastics. The exponential growth of AM in the worldwide polymer market is expected to exceed 20 billion US dollars by 2021 in areas of automotive, medical, aerospace, energy and customized consumer products. The development of functional polymers and composites by 3D printing-based technologies has been explored significantly due to its cost-effective, easier integration into customized geometries, higher efficacy, higher precision, freedom of material utilization as compared to traditional injection molding, and thermoforming techniques. Since polymers are the most explored class of materials in AM to overcome the limitations, this review describes the latest research conducted on petroleum-based polymers and their composites using various AM techniques such as fused filament fabrication (FFF), selective laser sintering (SLS), and stereolithography (SLA) related to 3D printing in engineering applications such as biomedical, automotive, aerospace and electronics.