Surface plasmon polaritons (SPPs) are electromagnetic (EM) modes propagating along metal-dielectric interfaces, in which surface collective excitations of free electrons in the metal are coupled to evanescent EM fields in the dielectric. Various SPP modes can be supported by flat and curved, single and multiple surfaces, exhibiting remarkable properties, including the possibility of concentrating EM fields beyond the diffraction limit, i.e. on the nanoscale, while enhancing local field strengths by several orders of magnitude. This unique feature of SPP modes, along with the ever-increasing demands for miniaturization of photonic components and circuits, generates an exponentially growing interest in SPP-mediated radiation guiding and SPP-based waveguide components. Here we review the current status of this rapidly developing field, starting with a brief presentation of the main planar SPP modes along with the techniques employed for their excitation and manipulation by sets of nanoparticles. We then describe in detail various SPP-based waveguide configurations that ensure two-dimensional mode confinement in the plane perpendicular to the propagation direction and compare their characteristics. Excitation of SPP waveguide modes and recent progress in the development of SPP-based waveguide components are also discussed, concluding with our outlook on challenges and possible future developments in this field.