This review summarizes the most recent advances from technological and physico-chemical perspectives to improve several remaining issues in polymeric materials’ additive manufacturing (AM). Without a doubt, AM is experimenting with significant progress due to technological innovations that are currently advancing. In this context, the state-of-the-art considers both research areas as working separately and contributing to developing the different AM technologies. First, AM techniques’ advantages and current limitations are analyzed and discussed. A detailed overview of the efforts made to improve the two most extensively employed techniques, i.e., material extrusion and VAT-photopolymerization, is presented. Aspects such as the part size, the possibility of producing parts in a continuous process, the improvement of the fabrication time, the reduction of the use of supports, and the fabrication of components using more than one material are analyzed. The last part of this review complements these technological advances with a general overview of the innovations made from a material perspective. The use of reinforced polymers, the preparation of adapted high-temperature materials, or even the fabrication of metallic and ceramic parts using polymers as supports are considered. Finally, the use of smart materials that enable the fabrication of shape-changing 3D objects and sustainable materials will also be explored.