Three-dimensional (3D) printing is becoming a booming technology to fabricate scaffolds, orthoses, and prosthetic devices for tissue engineering, regenerative medicine, and rehabilitation for patients with disabling neurological diseases (such as amyotrophic lateral sclerosis, traumatic brain injuries, and spinal cord injuries). This is due to the potential of 3D printing to provide patient-specific designs, high structural complexity, and rapid on-demand fabrication at a low-cost. However, one of the major bottlenecks that limits the widespread acceptance of 3D printing for biomedical manufacturing is the lack of polymers, biomaterials, hydrogels, and bioinks functional for 3D printing, biocompatible, and more performing from the biomechanical point of view to meet the different needs. As a matter of fact the field is still struggling with processing of such materials into self-supporting devices with tunable biomechanics, optimal structures, degradation, and bioactivity. Here, will be highlighted all recent advances that have been made in the field of 3D printing in biomedicine, analyzing the polymers, hydrogels, and bioinks, according to their printability, ease of processability, cost, and properties such as mechanics, biocompatibility, and degradation rate. Finally, future considerations for 3D bio-fabrication will be discussed.