Research and scholarship on sexuality has grown exponentially over the last 60 years; but what is this 'sexuality' that so fascinates us. During those 60 years, three academic traditions or paradigms have emerged and evolved to provide that main ways we understand sexuality. These are: (1) sexology; (2) sex research; and (3) critical sexuality studies. These paradigms do not always agree; at times, they are incommensurable in the picture of sexuality they paint. However, they each affect how sexuality is researched and written about, and how it is understood in the popular imagination. After discussing these paradigms, attention is focused on the contemporary challenges facing the third paradigm: critical sexuality studies. The contribution of sexology and sex research to these challenges is noted. Three key issues are discussed: the body; how we commonly understand sexuality; and the commodification of sexuality in late modernity.