3D printing is a rapidly growing technology that has an enormous potential to impact a wide range of industries such as engineering, art, education, medicine, and aerospace. The flexibility in design provided by this technique offers many opportunities for manufacturing sophisticated 3D devices. The most widely utilized method is an extrusion‐based solid‐freeform fabrication approach, which is an extremely attractive additive manufacturing technology in both academic and industrial research communities. This method is versatile, with the ability to print a range of dimensions, multimaterial, and multifunctional 3D structures. It is also a very affordable technique in prototyping. However, the lack of variety in printable polymers with advanced material properties becomes the main bottleneck in further development of this technology. Herein, a comprehensive review is provided, focusing on material design strategies to achieve or enhance the 3D printability of a range of polymers including thermoplastics, thermosets, hydrogels, and other polymers by extrusion techniques. Moreover, diverse advanced properties exhibited by such printed polymers, such as mechanical strength, conductance, self‐healing, as well as other integrated properties are highlighted. Lastly, the stimuli responsiveness of the 3D printed polymeric materials including shape morphing, degradability, and color changing is also discussed.