Moiré superlattices formed by angle-aligned multilayer stacks of 2D materials have recently become a rich platform to discover novel electronic states, such as superconductivity, correlated insulators, and magnetism. In this talk, I will talk about our recent work on the study of correlated states in moiré superlattices of semiconducting transition metal dichalcogenides monolayers. We employ scanning microwave impedance microscopy to probe the local conductivity of these moiré superlattices. We find that correlated insulating states can appear when the moiré superlattice is partially filled with carriers at simple fractional fillings. When additional layers are introduced in the moiré structure, we find that the correlated states can be manipulated in various ways. By applying an electric field, the carriers can be driven to populate in two different layers yet still form insulating states, which can be interpreted as an excitonic insulator. We perform a combination of optical spectroscopy and scanning probe microscopy measurements to reveal the nature of this state.