It has become possible in recent years to fabricate and manipulate two-dimensional nanomaterials in the laboratory that are as thin as one to few atomic layers. The reduced dimensionality gives rise to unique physical and chemical properties that differ from those of traditional bulk materials, and intriguing physics has been found in these few-layer systems. In this talk, I will focus on a few representative systems, including twisted bilayer graphene and monolayers of transition metal dichacogenides that exhibit properties ranging from normal semiconductors to charge density waves to superconductivity. I will discuss our recent theoretical and computational studies to explore the connections among charging, lattice distortion, electronic properties, charge density waves, and superconductivity.