Graphene is a monolayer of carbon atoms arranged in a honey-comb lattice: atomically thin, light, flexible, mechanically strong, visually transparent, electrically tunable, and highly conductive if doped. Graphene also interacts with light strongly from the microwave range to the ultraviolet, spanning wavelengths of at least five orders of magnitude. Such strong light-graphene interaction, together with its exceptional electronic and mechanical properties, makes graphene a promising candidate for various photonic applications. The early part of this paper addresses the physics of light-graphene interaction under a single-electron approximation, followed by a discussion of light excitation of collective oscillations of the carriers, i.e., plasmons in graphene. A variety of photonic devices operating in different wavelength ranges based on the two different light-graphene interaction mechanisms discussed above, such as photodetectors, optical modulators, electromagnetic wave shieldings, notch filters, and linear polarizers are then covered. Finally, we discuss the future directions for graphene photonics research.