Known approaches to modeling terahertz plasmons in two-dimensional electron sys-tems may differ significantly in their assumptions. There has, however, been littleeffort to analyze the differences between and application of different models to thesame sets of structures. This paper discusses, develops, and compares several differenttheoretical approaches—namely, an effective-medium approximation, a transmission-line model, modal analysis, and full-wave simulations. In particular, wepresent atransmission-line model that takes into account the dielectric/air surrounding of atwo-dimensional system. Using modal analysis, we also solve analytically the problemof plasmon reflection and transmission when plasmons are incident ona junction be-tween gated and an ungated two-dimensional waveguides. Comparing the predictionsmade by the models for several structures, we found good agreement between full-wave simulations and both analytical and numerical modal analysis. The results ofthe effective-medium approximation and the transmission-line modelalso agreed witheach other, but differed quantitatively from full-wave simulations and modal analysis.We attribute the differences to the phases of plasmon reflection and transmission co-efficients obtained using the different approaches. Our analytical expressions for theplasmon transmission and reflection coefficients represent a simple yet accurate way to model plasmons in two-dimensional systems comprising both gated and ungated sections.