Surface plasmon polaritons (SPPs) are electromagnetic modes propagating along metal-dielectric interfaces. Various SPP modes can be supported by flat and curved, single and multiple surfaces, exhibiting remarkable properties, including the possibility of concentrating electromagnetic 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 ever increasing demands for miniaturization of photonic components and circuits generates an exponentially growing interest to 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 main planar SPP modes, and then describing in detail various SPP-based waveguide configurations that ensure two-dimensional mode confinement. Excitation of SPP waveguide modes and recent progress in development of SPP-based waveguide components is also discussed, concluding with our outlook on challenges and possible future developments in this field.