Surface plasmon polaritons (SPPs) are evanescent waves propagating along metal-dielectric interfaces, which provide an effective way to realize optical wave guiding with subwavelength confinement. Metallic nanostructures supporting SPPs, that is, plasmonic waveguides, are considered as required components to construct nanophotonic devices and circuits with a high degree of miniaturization and integration. In this paper, various types of plasmonic waveguides operating in the visible, infrared, and terahertz regions are reviewed, and the status of the research on their fundamentals, fabrications, and applications is provided as well. First, we discuss the mechanisms of SPPs beyond the diffraction limit, and their launching methods. Then, the characteristics of SPPs on various plasmonic waveguides are reviewed, including top-down and bottom-up fabricated types. Considering applications, certain prototypes of plasmonic devices and circuits constructed by plasmonic waveguides for bio/chemo sensing, router, and light modulation are demonstrated. Finally, a summary and future outlook of plasmonic waveguides are given.