This paper aims to provide a comprehensive survey of recent advancements in modelling and autonomous manipulation of non-rigid objects. It first summarizes the recent advances in sensing and modelling of such objects with a focus on describing the methods and technologies used to measure their shape and estimate their material and physical properties. Formal representations considered to predict the deformation resulting from manipulation of non-rigid objects are then investigated. The third part provides a survey of planning and control strategies exploited to operate dexterous robotic systems while performing various tasks on objects made of different non-rigid materials.