In this paper, aerodynamic decelerators are defined as textile devices intended to be deployed at Mach numbers below five. Such aerodynamic decelerators include parachutes and inflatable aerodynamic decelerators (often known as ballutes). Aerodynamic decelerators play a key role in the Entry, Descent, and Landing (EDL) of planetary exploration vehicles. Among the functions performed by aerodynamic decelerators for such vehicles are deceleration (often from supersonic to subsonic speeds), minimization of descent rate, providing specific descent rates (so that scientific measurements can be obtained), providing stability (drogue function -either to prevent aeroshell tumbling or to meet instrumentation requirements), effecting further aerodynamic decelerator system deployment (pilot function), providing differences in ballistic coefficients of components to enable separation events, and providing height and timeline to allow for completion of the EDL sequence. Challenging aspects in the development of aerodynamic decelerators for planetary exploration missions include: deployment in the unusual combination of high Mach numbers and low dynamic pressures, deployment in the wake behind a blunt-body entry vehicle, stringent mass and volume constraints, and the requirement for high drag and stability. Furthermore, these aerodynamic decelerators must be qualified for flight without access to the exotic operating environment where they are expected to operate. This paper is an introduction to the development and application of aerodynamic decelerators for robotic planetary exploration missions (including Earth sample return missions) from the earliest work in the 1960s to new ideas and technologies with possible application to future missions. An extensive list of references is provided for additional study.