Polymers have a long history in medicine. Their uses to date range from traditional applications such as catheters, syringes, blood contacting extra corporeal devices to matrices for drug delivery, cell encapsulation and tissue regeneration. Polymers can be broadly classified on the basis of the reactivity of their chemical backbone (or susceptibility of the backbone to breakdown upon exposure to water, i.e., hydrolysis) as non-degradable and degradable. In this review, the polymers that exhibit no to very low degradation in aqueous and biological environments will be covered. The applications of various polymers both in traditional and emerging medical areas is discussed in the context of its chemical structure to better enable material selection for biomedical research.