Summary: This paper documents some of the historical steps in the development of the concept of procept. It then describes how these ideas have led to the construction of an emerging theoretical perspective on what constitutes versatile mathematical thinking and learning. Three parts of this theory are presented: process/object versatility; visuo/analytic versatility and representational versatility. Each of these aspects is illuminated by the use of data and examples gleaned from research projects in areas as diverse as algebra, calculus, linear algebra and statistics. It is hoped that it will be possible to infer how this developing conception of versatile mathematical thinking can be fostered and promoted in students.