Despite the fact that most of us value integrity, and despite the fact that we readily understand one another when we talk and argue about it, integrity remains elusive to understand. Considerable scholarly attention has left troubling disagreement on fundamental issues: Is integrity in fact a virtue? If it is, what is it a virtue of? Why exactly should we value integrity? What is the appropriate way to have concern for one’s own integrity? Is having integrity compatible with having significant moral flaws? After an overview of common ‘data points’ or platitudes concerning integrity, this article outlines six distinct views of integrity that have been defended and draws attention to problems each has accommodating these data points.