In recent years, we have seen a rapid progress in the field of graphene plasmonics, motivated by graphene's unique electrical and optical properties, tunability, long-lived collective excitation and its extreme light confinement. Here, we review the basic properties of graphene plasmons: their energy dispersion, localization and propagation, plasmon-phonon hybridization, lifetimes and damping pathways. The application space of graphene plasmonics lies in the technologically significant, but relatively unexploited terahertz to mid-infrared regime. We discuss emerging and potential applications, such as modulators, notch filters, polarizers, mid-infrared photodetectors, and mid-infrared vibrational spectroscopy, among many others. © 2014 American Chemical Society.