Self-assembled monolayers (SAMs) of alkanethiols and dialkanethiols on gold are key elements for building many systems and devices with applications in the wide field of nanotechnology. Despite the progress made in the knowledge of these fascinating two-dimensional molecular systems, there are still several "hot topics" that deserve special attention in order to understand and to control their physical and chemistry properties at the molecular level. This critical review focuses on some of these topics, including the nature of the molecule-gold interface, whose chemistry and structure remain elusive, the self-assembly process on planar and irregular surfaces, and on nanometre-sized objects, and the chemical reactivity and thermal stability of these systems in ambient and aqueous solutions, an issue which seriously limits their technological applications (375 references).