The two-dimensional atomic crystals (2DACs) of transitional metal dichalcogenides (e.g., MoS2, MoSe2, WS2 and WSe2) have attracted intense recent interest. With a nearly perfect crystalline structure and dangling bond free surface, these atomically thin materials have emerged as a new material platform for fundamental materials science and diverse technology opportunities at the limit single atomic thickness. To explore the full potential of these 2DACs requires the integration of highly disparate materials and the construction of heterostructures with designed spatial modulation of chemical compositions and electronic structures, much like the traditional semiconductor heterostructures and superlattices that form the fundamental material foundation for all modern electronic and optoelectronic devices. The traditional material integration approach to create the heterostructures from such atomically thin materials can often lead to considerable damage to the lattice structure and compromise their intrinsic properties. Considerable efforts have been devoted to produce various 2DAC heterostructures by using either a van der Waals assembly approach or synthetic chemistry approach. Here I will discuss our recent efforts in exploring various 2DAC heterostructures and devices.