We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we investigate a sequence of models that have an interaction effect and/or variable centering and derive expressions for the change in the regression coefficients between models from both an intuitive and mathematical perspective. We demonstrate how these topics may be employed to motivate discussion of other important areas, e.g., misspecification bias, multicollinearity, design of experiments, and regression surfaces. This paper presents a number of results also given elsewhere but in a form that gives a unified view of the topic. The examples cited are from the area of medical statistics. (Contains 5 figures, 3 tables and 15 footnotes.)