This paper focuses on polymers that demonstrate microporosity without possessing a network of covalent bonds-the so-called polymers of intrinsic microporosity (PIM). PIMs combine solution processability and microporosity with structural diversity and have proven utility for making membranes and sensors. After a historical account of the development of PIMs, their synthesis is described along with a comprehensive review of the PIMs that have been prepared to date. The important methods of characterising intrinsic microporosity, such as gas absorption, are outlined and structure-property relationships explained. Finally, the applications of PIMs as sensors and membranes for gas and vapour separations, organic nanofiltration, and pervaporation are described.