Since the early 90s, adhesive contact mechanics has emerged as an area of considerable interest in nano- and bio-sciences. Here we review the methods which have been developed in the past 75 years to account for adhesive interactions in elastic contact problems. Emphasis is given to the connexion between the local, physical mechanism of adhesion and the macroscopic, mechanical loading. The discussion centers on the contact equations. In an attempt to provide a broad view of the field, we outline the key concepts and their progressive developments, starting from the approximate calculation by Derjaguin in 1934 and ending with recent results for coated systems and time dependent materials, through the well established DMT and JKR models.