A web is a material whose length is much in excess of the width and the width is much larger than the thickness. Various grades of paper, plastic films, metal foils and laminates can all be broadly categorized as webs. Web media are often stored for periods of time in the form of a wound roll. This form of storage is chosen because it is simply the most convenient and often the only form for storing vast lengths of web with minimal damage and loss. Winding can damage the web and has become a topic which has received considerable attention in the literature. Amongst operations in a web process line, the winder and the unwinder are often sites at which web defects appear that may result in a loss of quality or may lead to a break or burst of the web resulting in lost productivity. The purpose of this paper is to review the state of the science of winding and unwinding rolls. The threads of pertinent information in the literature focus on: the stresses that are wound into rolls, how those stresses are affected by the type of winder employed, how those stresses vary during roll storage, how the stresses predicted by models can be used to predict wound roll defects, and finally the measurements that are available to verify modeling efforts or help solve production problems. Each thread will be examined in this review from the perspective of what references exist but also giving enough detail that an appreciation for the significance of a topic can be developed.