Graphene, a single layer material of carbon atoms in a two-dimensional honeycomb lattice nanostructure, is a promising electro-optic material platform, since its optical conductivity is tunable via carrier density modulation and its carrier density is easily tunable via electric field-effect gating. Integrated with metasurfaces---thin membranes (dielectric or metallic) artificially structured with on-demand patterns, graphene can be made even more versatile for advanced electro-optic applications. In particular, this dissertation focuses on engineering the optical properties in graphene-metasurface structures based on plasmonic resonances in the integrated systems. These plasmonic resonances can be hosted by a metallic metasurface and marginally controlled by graphene (the first chapter). In contrast, the plasmons can be primarily carried by graphene itself and controlled by metasurfaces (the second chapter). More interestingly, the interplay between graphene and metasurfaces can lead to a completely new type of optical resonances hybridized with the underlying plasmonic resonances (the third chapter). Through the survey of these distinct scenarios, this dissertation aims to show how graphene-based plasmonic metasurfaces can be used for the study of a wide range of electro-optics research focuses such as optical sensing devices, active topological photonics, and gate-tunable intersubband-polaritons. In the first chapter, a graphene-integrated metasurface structure is used as a polarimeter of mid-infrared light. A plasmonic metasurface is designed to have anisotropic reflection coefficients for the light incident on it, so that the polarization state of light would change upon the reflection. Then, through the gate-tuning of graphene placed right below the metasurface, the polarization state change upon reflection can be given as a function of the gate voltage. If this polarization state change is fully characterized at a range of gate voltages, a polarimetric measurement can be done on an incident light with unknown polarization state by recording the intensity of reflected light as a function of gate voltage and fitting the intensity-voltage curve to the fully characterized model. This work proves graphene as an excellent electro-optic modulator element for electro-optical sensing device applications. In the second chapter, on the other hand, a metallic metasurface is used as a modulator that controls the property of optical modes confined at graphene---graphene plasmon-polaritons. In fact, the metallic metasurface is used only for the field-effect gating purpose, rather than for its own plasmonic resonances. For this reason, this metallic metasurface is called a metagate. When graphene is doped through a metagate, the periodic shape in the metagate is imprinted to the landscape of modulated carrier densities on graphene. Since the dispersion relation of graphene plasmon-polaritons depends on the carrier density, the modulated carrier density pattern serves as a photonic crystal structure. By a proper design of the metagate, graphene plasmon-polaritons acquire topological band structures and feature topologically protected edge states inside the photonic (plasmonic) bandgap. This proposal of metagate-based approach to graphene plasmonics has been already demonstrated in recent experimental works. In the third chapter, a more rigorous analysis of a metagate-tuned graphene system is carried out, taking into consideration the deformation of the electronic band structure in graphene as well. It turns out that, with a one-dimensional metagate-superlattice potential, the Dirac electrons in graphene experience total internal reflection within the in-plane potential wells, forming several bound states. As these bound states constitute flat subbands in the band structure, the resulting optical conductivity of graphene shows an emergent intersubband transition responses. Graphene plasmon-polaritons then interact resonantly with intersubband transitions, thereby giving rise to hybrid intersubband-plasmon-polaritons. This example shows that the interaction between graphene and metasurface can lead to an emergent electro-optic phenomenon beyond naturally expected perturbative effects.