Realizing the full potential of any materials system requires understanding and controlling disorder, which can obscure intrinsic properties and hinder device performance. Here we examine both intrinsic and extrinsic disorder in two-dimensional (2D) materials, in particular graphene and transition metal dichalcogenides (TMDs). Minimizing disorder is crucial for realizing desired properties in 2D materials and improving device performance and repeatability for practical applications. We discuss the progress in disorder control for graphene and TMDs, as well as in van der Waals heterostructures realized by combining these materials with hexagonal boron nitride. Furthermore, we showcase how atomic defects or disorder can also be harnessed to provide useful electronic, optical, chemical and magnetic functions.