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This paper studies the guided-wave transmission of terahertz electromagnetic waves along the surface waveguides and parallel-plate waveguides (PPWGs). Field analysis is presented to show that low-loss and quasi-TEM propagation is only possible when the waveguides are operating in their plasmonic modes. It is shown that the observed low-loss and quasi-TEM propagation of terahertz waves in the PPWGs is due to resonant coupling of surface plasmons between the two plates. Transmission line models based on the peculiar characteristics of the surface waves associated with the plasmonic modes of the guides are developed and the distinctions with the conventional transmission line theory are highlighted.