Recent decades have seen great advancements in medical research into materials, both natural and synthetic, that facilitate the repair and regeneration of compromised tissues through the delivery and support of cells and/or biomolecules. Biocompatible polymeric materials have become the most heavily investigated materials used for such purposes. Naturally‐occurring and synthetic polymers, including their various composites and blends, have been successful in a range of medical applications, proving to be particularly suitable for tissue engineering (TE) approaches. The increasing advances in polymeric biomaterial research combined with the developments in manufacturing techniques have expanded capabilities in tissue engineering and other medical applications of these materials. This review will present an overview of the major classes of polymeric biomaterials, highlight their key properties, advantages, limitations and discuss their applications. © 2014 Society of Chemical Industry