Maxillofacial defects, arising from trauma, oncological disease or congenital differences, detrimentally affect everyday life. Prosthetic repair offers the aesthetic and functional reconstruction with the help of materials mimicking natural tissues, among which polymers take unprecedented role. The three-dimensional (3D) printing techniques based on the computer-aided design, where polymers are essential, provide a rapid and cost-effective workflow protocol to perfectly restore patient-specific anatomy for prosthetics. This review discusses the main 3D printing approaches to maxillofacial prostheses fabrication: extrusion and lithography, which are radically preferable to the traditional methods. The main assessment criteria, affording the polymer implementation in 3D printing of prostheses, as well as the characteristics of the key advanced polymers, are considered. The success of the prosthesis is shown to be largely dependent on the retention system, predominantly using polymers in the form of adhesives and osseointegrated implants as a support for the prosthesis. The approaches and technological prospects are also discussed in the context of specific aesthetic restoration on the example of the nasal, auricle and ocular prostheses. 3D printing techniques determine the development of personalized approaches to improve aesthetic and functional effect of prosthetics in patients with maxillofacial defects.