We review dynamic quality models both in single-agent setup and in a competitive framework. Our objectives are: (1) to give the reader a vantage point on the state of the art in this area, (2) to identify the boundaries between the different concepts of quality to help build a bridge between the various communities interested in the management of quality, and (3) to sketch out a research agenda for the area. The paper should not only be of interest to active researchers in the field, but also to a broader community of scholars and practitioners working in operations management, marketing, industrial engineering and operations research, who are interested in quality dynamics.