Surface plasmons are collective oscillations of electrons in metals or semiconductors that enable confinement and control of electromagnetic energy at subwavelength scales1, 2, 3, 4, 5. Rapid progress in plasmonics has largely relied on advances in device nano-fabrication5, 6, 7, whereas less attention has been paid to the tunable properties of plasmonic media. One such medium—graphene—is amenable to convenient tuning of its electronic and optical properties by varying the applied voltage8, 9, 10, 11. Here, using infrared nano-imaging, we show that common graphene/SiO2/Si back-gated structures support propagating surface plasmons. The wavelength of graphene plasmons is of the order of 200nanometres at technologically relevant infrared frequencies, and they can propagate several times this distance. We have succeeded in altering both the amplitude and the wavelength of these plasmons by varying the gate voltage. Using plasmon interferometry, we investigated losses in graphene by exploring real-space profiles of plasmon standing waves formed between the tip of our nano-probe and the edges of the samples. Plasmon dissipation quantified through this analysis is linked to the exotic electrodynamics of graphene10. Standard plasmonic figures of merit of our tunable graphene devices surpass those of common metal-based structures.