The Fourier restriction inequalities originate from the work of Stein, Tomas, Strichartz and Sigal in the 1970s, and imposed themselves as a cornerstone of modern harmonic analysis. In these three talks we will present the state of the art for the problem of determining these inequalities in sharp form, that is, with best possible constants and knowledge of the functions which attain them. We will explore a selection of recent results with detailed proofs.