This paper aims to present a review of recent progress made on shape memory polymers (SMPs) and their nanocomposites. Developments in allied fields are also presented in an effort to identify the current and future trends in this area. A new classification of SMP--rubberlike and mesomorphic systems--is suggested. The underlying physical mechanisms of shape memory actions, polymer-nanofiller interactions, and the resultant properties of SMP nanocomposites are discussed. Examples are presented to highlight the influence of processing conditions, filler geometry and filler surface characteristics, and the nature of matrix polymers on shape memory properties. A short description of current and potential applications is also presented.