Graphene, the one-atom-thick carbon crystal, represents the first of an entire class of two-dimensional materials. In this thesis, the opportunities of graphene as a building block for optoelectronics and metamaterials are explored.Several key frontiers of graphene research specifically for the applications in optoelectronics and metamaterials are addressed. The first frontier, which concerns the understanding of the fundamental optical properties of graphene, is investigated using experimental methods. In one of the projects, experiments are conducted to study the nonlinear harmonic generation of graphene at terahertz frequencies. 10-layer epitaxial graphene is excited with 40 kV/cm terahertz fields but no harmonic generation with an efficiency greater than 2% is observed. This result reveals the fundamental role played by the strong carrier-carrier scattering, which had been neglected by previously published theories of nonlinearity. Another project develops an ellipsometry-based technique that allows for accurate and robust measurement of the optical conductivities of two-dimensional materials. Measurements of the optical conductivities of mono- and bilayer graphene from the ultraviolet to mid-infrared range are demonstrated. This technique is also applied to study the effect of chemical doping on the optical conductivity of graphene.Another class of projects aims to push the second frontier of graphene research — the new opportunities in physics and applications enabled by the fabrication of complex graphene layered structures. These include the development of a double-layer graphene photodetector, which achieves broadband infrared operation and high responsivity on the order of A/W utilizing the phototransistor gain, and the realization of vertically-stacked graphene-dielectric multilayers, which turns into a hyperbolic metamaterial for wavelengths longer than 4.5 μm.The third frontier of graphene research addressed in this thesis investigates the combination of graphene with metasurfaces, as graphene and metasurfaces share the same reduced dimensionality compared to their bulk counterparts. A new type of metasurface based on the guided resonance of a photonic hypercrystal is proposed, which can serve as a two-dimensional resonator for enhancing the light-graphene interaction. Using full-wave electromagnetic simulation, it is demonstrated that the combined system can create optical modulators with high modulation depth and photodetectors with enhanced absorption.