Non-degradable polymers have an important function in medicine. Solid dosage forms for longer term implantation require to be constructed from materials that will not degrade or erode over time and also offer the utmost biocompatibility and biostability. This review details the three most important non-degradable polymers for the production of solid dosage forms - silicone elastomer, ethylene vinyl acetate and thermoplastic polyurethane. The hydrophobic, thermoset silicone elastomer is utilised in the production of a broad range of devices, from urinary catheter tubing for the prevention of biofilm to intravaginal rings used to prevent HIV transmission. Ethylene vinyl acetate, a hydrophobic thermoplastic, is the material of choice of two of the world's leading forms of contraception - Nuvaring® and Implanon®. Thermoplastic polyurethane has such a diverse range of building blocks that this one polymer can be hydrophilic or hydrophobic. Yet, in spite of this versatility, it is only now finding utility in commercialised drug delivery systems. Separately then one polymer has a unique ability that differentiates it from the others and can be applied in a specific drug delivery application; but collectively these polymers provide a rich palette of material and drug delivery options to empower formulation scientists in meeting even the most demanding of unmet clinical needs. Therefore, these polymers have had a long history in controlled release, from the very beginning even, and it is pertinent that this review examines briefly this history while also detailing the state-of-the-art academic studies and inventions exploiting these materials. The paper also outlines the different production methods required to manufacture these solid dosage forms as many of the processes are uncommon to the wider pharmaceutical industry.