Conventional semiconductors (e.g. Silicon and Gallium Arsenide) and their heterostructures are the foundation of condensed matter physics and present solid-state technologies, such as light emitting diodes, solar cells, and high speed transistors. Recently, new classes of quantum materials at 2-dimensional limit have been discovered, including atomically thin monolayers of graphite, boron nitride, and transition metal dichalcogenides (TMDs). These monolayer materials not only have remarkable physical properties on their own, but also they can be stacked together to form van der Waals heterostructures for new functionalities, offering unprecedented opportunities to explore new realms in materials science, device physics, and engineering. In this talk, I will focus on 2-dimensional semiconductors and their heterostructures. Fundamentally new properties in these structures include the relationship between electron spin, the "valley index" specifying which of the two inequivalent momentum states the electron occupies in the 2D lattice, and the "layer index" specifying which layer the electron is in when two monolayers form a bilayer. I will discuss the experimental progress towards understanding and optoelectronic control of spins and pseudospins in both monolayers and atomically-thin semiconducting heterostructures.