Two-dimensional (2D) atomic layers derived from bulk layered materials are very interesting from both scientific and application viewpoints, as evidenced from the story of graphene. Atomic layers of several such materials such as hexagonal boron nitride (h-BN) and dichalcogenides are examples that complement graphene. The observed unconventional properties of graphene has triggered interest in doping the hexagonal honeycomb lattice of graphene with atoms such as boron (B) and nitrogen (N) to obtain new layered structures. Individual atomic layers containing B, C, and N of various compositions conform to several stable phases in the three-component phase diagram of B-C-N. Additionally, stacking layers built from C and BN allows for the engineering of new van-der-Waals stacked materials with novel properties. In this paper, the synthesis, characterization, and properties of atomically thin layers, containing B, C, and N, as well as vertically assembled graphene/h-BN stacks are reviewed. The electrical, mechanical, and optical properties of graphene, h-BN, and their hybrid structure are also discussed along with the applications of such materials.