A review of the chemical structures, physical properties, and current and potential applications of liquid crystalline polymers (LCPs) is presented. Comparisons are made between LCPs, low molecular weight liquid crystals (LCs), and conventional polymers for readers unfamiliar with the field. The ordered liquid phases are classified and molecular requirements for the formation of LC phases in both LCP melts (thermotropics) and LCP solutions (lyotropics) are discussed. The theoretical predictions of the formation of ordered phases given by Flory and Onsager are compared with experimental data, and other aspects of the phase behaviour of LCPs in solution are considered, including physical gelation and crystal-solvate complexes. A wide variety of polymer structures that exhibit LC behaviour are presented. These include main chain (rigid rod), semiflexible, main chain with flexible spacers, and side chain LCPs, and various new combinations that have been recently devised. An emphasis is placed on the relationship between chemical and physical structure of LCPs, rather than on the details of the synthesis. The unique physical properties of these materials, including the rheological or flow behaviour, optical, electrical, and mechanical properties, and possible applications in blends, composites, optical devices, elastomers, and other areas are highlighted.