Most scholars of purchasing and supply management (PSM) are familiar with some form of a purchasing process model (PPM). A PPM is the visual representation of the sequence of activities that constitute purchasing and supply management. Such a visual representation can be a tool in teaching PSM since it gives students an overview of an otherwise intangible process. Moreover, a PPM can also be viewed as a representation of the identity of PSM, providing a schema of what is PSM (and what it is not). In this notes and debates article, a systematic overview of different types of PPMs, and their evolution, is presented, based on a literature review and a survey, with the models being classified as tactical/operational, strategic, cyclical, or decision-making processes. Our first aim is to inspire PSM scholars and educators when they are considering various PPMs to be used in their teaching of PSM. Our second aim is to debate the question where the evolution of PPMs is heading and explore whether a single holistic model can provide an accurate and representative framework to structure purchasing activities both today and in the future.