The understanding of various types of disorders in 2D materials, including dangling bonds at the edges, defects in the bulk, and charges in the substrate, is of fundamental importance for their applications in electronics and photonics. Because of the imperfections, electrons moving on the 2D plane experience a spatially non-uniform Coulomb environment, whose effect on the charge transport has not been microscopically probed. Using a non-invasive microwave impedance microscope with ~100nm resolution and ~1nS sensitivity, we can visualize the spatial evolution of the insulator-to-metal transition in mono-layer and few-layer MoS2 field-effect transistors. As the transistors are gradually turned on, electrical conduction emerges initially at the edges before appearing in the bulk, which can be explained by first-principles calculations. The topologically trivial edge states are to be compared with the nontrivial edges in quantum Hall and quantum spin Hall states. Strong electrical inhomogeneity is observed in the MIM images, revealing the fluctuations of disorder potential in the 2D sheets. I will also discuss the conductance mapping in ion-gel-gated electric double-layer transistors and 2D devices under laser illumination. The combination of novel FETs and impedance microscopy paves the way to study phase transitions in complex materials induced by electrostatic field effects.