Piezoelectric materials can directly transduce electrical and mechanical energy, making them attractive for applications such as sensors, actuators and energy harvesting devices. While often associated with ceramic materials, piezoelectric behaviour is also observed in many polymers. The flexibility, ease of processing and biocompatibility of piezoelectric polymers mean that they are often preferable for certain applications, despite their lower piezoelectric coefficients. This review will cover some theoretical and practical concepts of piezoelectricity in polymers, such as the symmetry requirements, the underlying mechanism and the necessary materials processing. A brief review of the applications of piezoelectric polymers is also presented. One of the main motivations of this review is to discuss the challenges and open questions in the field in an effort to highlight potential future research directions.