In this article, we discuss the recent progress on controlled structural modification of 2D materials by means of molecular functionalization, with a focus on scanning probe microscopy techniques for their characterization. For many practical applications of these novel materials, it is necessary to tune their electronic and optical properties, and molecule-based functionalization is a powerful approach to reach this. We discuss recent covalent and non-covalent approaches, for functionalization of graphene, transition metal dichalcogenides, black phosphorus, and hexagonal boron nitride. Nanostructuring approaches and their impact on 2D materials' properties are highlighted.