3D printing is a state-of-the-art technology for the fabrication of biomaterials with myriad applications in translational medicine. After stimuli-responsive properties were introduced to 3D printing (known as 4D printing), intelligent biomaterials with shape configuration time-dependent character have been developed. Polysaccharides are biodegradable polymers sensitive to several physical, chemical, and biological stimuli, suited for 3D and 4D printing. On the other hand, engineering of mechanical strength and printability of polysaccharide-based scaffolds along with their aneural, avascular, and poor metabolic characteristics need to be optimized varying printing parameters. Multiple disciplines such as biomedicine, chemistry, materials, and computer sciences should be integrated to achieve multipurpose printable biomaterials. In this work, 3D and 4D printing technologies are briefly compared, summarizing the literature on biomaterials engineering though printing techniques, and highlighting different challenges associated with 3D/4D printing, as well as the role of polysaccharides in the technological shift from 3D to 4D printing for translational medicine.