Student engagement is a complex phenomenon, with diverse interpretations, even within further and higher education. This article presents three potential, interconnected, novel models which provide a measure of unification of the range of interpretations and hence may improve understanding of the broad phenomenon. The models emerged from a study of computing students but should be relevant across a wide range of disciplines. They are presented as being provisional but they should be useful in providing modifiable frameworks for the investigation of engagement issues and in student support activity. The first model is in the form of a force-field diagram, identifying forces which drive for, and those which drive against, student engagement. The second identifies four possible levels of student engagement created by an individual's responses to those forces. The final model represents an individual student's engagement as comprising four dimensions, encompassing forms of motivation and connectedness. In addition to these models, this article suggests that some students who may appear to be disengaged should more accurately be considered to be 'differently engaged'.