Graphene is a novel material that features a quasi-relativistic linear energy dispersion with the quantum mechanical motion of electrons obeying the massless Dirac equation. In this dissertation, we study the many-body effects in graphene due to Coulomb interaction and electron-phonon interaction. Interaction effects can appear in both transport and electronic properties. For many-body effects in transport, we formulate the theory for Coulomb drag in double-layer graphene. We calculate the drag resistivity and study its dependence on temperature, density and interlayer spacing, finding zero drag if one of the graphene layers is intrinsic (i.e., undoped) and a non-zero drag exhibiting a similar behavior to regular bilayer drag if both graphene layers are extrinsic (i.e., doped). For many-body effects in electronic properties, we formulate the theory for quasiparticle and phonon renormalization due to Coulomb and electron-phonon interaction. We first study renormalization of electron properties due to Coulomb interaction by calculating the renormalized quasiparticle parameters from the electron self-energy, showing that intrinsic graphene behaves as a marginal Fermi liquid and extrinsic graphene behaves as a regular Fermi liquid. We then study renormalization of electron properties due to electron-phonon interaction. We calculate the electron self-energy and the renormalized quasiparticle velocity, finding that the renormalized band structure exhibits a kink at the phonon energy in agreement with angle-resolved photoemission spectroscopy (ARPES) experiment. We finally study renormalization of phonon energy due to electron-phonon interaction. We calculate the phonon self-energy and the renormalized phonon energy dispersion, showing that multiple Kohn anomalies arise which are completely different from the Kohn anomaly in usual metals.