Airy beams represent an important class of nondiffracting waves which can be realized on a flat surface. Being generated in the form of surface-plasmon polaritons, such Airy plasmons demonstrate many remarkable properties: they do not diffract while propagating along parabolic trajectories, and they recover their shape after passing through obstacles. This paper reviews the basic physics of Airy plasmons in both paraxial and non-paraxial cases, and describes the experimental methods for generation of Airy surface waves on metal surfaces, including a control of their trajectories, as well as the interference of Airy plasmons and hot-spot generation. Many unusual properties of Airy plasmons can be utilized for useful applications, including plasmonic circuitry and surface tweezers. Picture: Observation of two colliding Airy plasmons.