Each year, congenital defects, trauma or cancer often results in considerable physical disfigurement for many people worldwide. This adversely impacts their psychological, social and economic outlook, leading to poor life experiences and negative health outcomes. In many cases of soft tissue disfigurement, highly personalized prostheses are available to restore both aesthetics and function. As discussed in part A of this review, key to the success of any soft tissue prosthetic is the fundamental properties of the materials. This determines the maximum attainable level of aesthetics, attachment mechanisms, fabrication complexity, cost, and robustness. Since the early-mid 20th century, polymers have completely replaced natural materials in prosthetics, with advances in both material properties and fabrication techniques leading to significantly improved capabilities. In part A, we discussed the history of polymers in prosthetics, their ideal properties, and the application of polymers in prostheses for the ear, nose, eye, breast and finger. We also reviewed the latest developments in advanced manufacturing and 3D printing, including different fabrication technologies and new and upcoming materials. In this review, Part B, we detail the chemistry of the most commonly used synthetic polymers in soft tissue prosthetics; silicone, acrylic resin, vinyl polymer, and polyurethane elastomer. For each polymer, we briefly discuss their history before detailing their chemistry and fabrication processes. We also discuss degradation of the polymer in the context of their application in prosthetics, including time and weathering, the impact of skin secretions, microbial growth and cleaning and disinfecting. Although advanced manufacturing promises new fabrication capabilities using exotic synthetic polymers with programmable material properties, silicones and acrylics remain the most commonly used materials in prosthetics today. As research in this field progresses, development of new variations and fabrication techniques based on these synthetic polymers will lead to even better and more robust soft tissue prosthetics, with improved life-like aesthetics and lower cost manufacturing.