The use of additive manufacturing (AM) has moved well beyond prototyping and has been established as a highly versatile manufacturing method with demonstrated potential to completely transform traditional manufacturing in the future. In this paper, a comprehensive review and critical analyses of the recent advances and achievements in the field of different AM processes for polymers, their composites and nanocomposites, elastomers and multi materials, shape memory polymers and thermo-responsive materials are presented. Moreover, their applications in different fields such as bio-medical, electronics, textiles, and aerospace industries are also discussed. We conclude the article with an account of further research needs and future perspectives of AM process with polymeric materials.