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Plasmonic circuit elements, which are based on complementary waveguide structures (waveguides with a dielectric core and metal cladding), are becoming preferred plasmonic devices for applications. In this paper, we look into the modeling of such devices, namely 1D waveguides and related elements as well as 2D slots, trenches, and channels supporting plasmonic slow waves. Methods such as the effective index, finite-difference time domain, finite elements, or other full-vectorial propagation schemes are among the methods discussed, and their limitations in the field of plasmonics are set. We believe that although many successful validated modeling methods were presented intensive efforts are still required for perfecting the various tools to faithfully describe nanosized plasmonic wave propagation on high-contrast nanometal discontinuities.