Two-dimensional (2D) materials, such as graphene and transition-metal dichalcogenide monolayers, have unique properties that are distinctly different from those of their bulk counterparts, and hopefully possess a wide range of applications in 2D semiconductor device. Structural defects are known to have profound influences on the properties of crystalline materials; thus, correlating the defect structure with local properties in 2D material is of fundamental importance. However, electron microscopy studies of 2D materials on an atomic scale have become a challenge as most of these materials are susceptible to electron beam irradiation damage under high voltage and high dose experimental conditions. The development of low voltage aberration-corrected scanning transmission electron microscopy (STEM) has made it possible to study 2D materials at a single atom level without damaging their intrinsic structures. In addition, controllable structural modification by using electron beam becomes feasible by controlling the electron beam-sample interaction. New nanostructures can be created and novel 2D materials can be fabricated in-situ by using this approach. In this article, we review some of our recent studies of graphene and transition-metal dichalcogenides to showcase the applications of low voltage aberration corrected STEM in 2D material research.