Since the mechanical isolation of graphene in 2004, studies of atomically-thin two-dimensional (2D) crystals have evolved into a vibrant field with many interesting discoveries and surprises. In this talk, I will discuss our recent studies of optical response of these fascinating 2D materials using a variety of light sources and techniques. The electrical outputs of graphene under electromagnetic wave excitation provide a basis for developing high performance sensors, especially in the mid- and far-infrared frequency ranges. These detectors are highly sensitive, fast and have very large bandwidth. The optical outputs of 2D crystals under laser excitation provide fundamental optical fingerprints and offer an appealing venue for investigating many-body physics. In monolayer transition metal dichalcogenide (TMDC) semiconductors, the inherent Coulomb interaction of the high-quality samples we fabricate enables us to observe photoluminescence (PL) due to two-, three-, four- and five-particle bound states. We unambiguously determine the spin and valley composition of these states. The PL further reveals 2s, 3s and 4s excited Rydberg states in high magnetic fields up to 31 Tesla. These studies pave way for new opportunities to build valleytronic quantum devices, and quantum communication platforms harnessing unique TMDC properties.