Graphene plasmons have aroused a great deal of research interest in recent years due to their unique features such as electrical tunability, ultra-strong field confinement and relatively low intrinsic damping. In this review paper, we summarize the fundamental optical properties of localized and propagating plasmons supported by graphene, and the experimental techniques for excitation and detection of them, with focusing on their dispersion relations and plasmon-phonon coupling mechanism. In general, the dispersion of graphene plasmons is affected by the Fermi level of graphene and the dielectric environment. The graphene plasmons can exist in a broad spectrum range from mid-infrared to terahertz. This has been experimentally verified for both the localized and propagation plasmons in graphene. On the one hand, the excitation frequency and confinement of localized plasmons supported by graphene micro/nano-structures are constrained by the structural geometry. Additionally, influenced from the tunability of the optical conductivity of graphene, the excitation frequency of graphene plasmons can be tuned by electrostatic or chemical doping. On the other hand, propagating plasmons have been launched and detected by using scattering-type scanning near-field optical microscopy. This technique provides the real-space imaging of the electromagnetic fields of plasmons, thereby directly confirming the existence of the graphene plasmons and verifying their properties predicted theoretically. In a similar regime, the launching and controlling of the propagating plasmons have also been demonstrated by using resonant metal antennas. Compared to metal plasmons, graphene plasmons are much more easily affected by the surroundings due to their scattering from impurity charges and coupling with substrate phonons. In particular, graphene plasmons can hybridize strongly with substrate phonons and there are a series of effects on plasmon properties such as resonance frequency, intensity and plasmon lifetime. The designing of the dielectric surrounding can effectively manipulate the graphene plasmons. Finally, we review the emerging applications of graphene plasmon in the mid-infrared and terahertz, such as electro-optical modulators and enhanced mid-infrared spectroscopy.