Extensive theoretical work has been performed on the equilibrium structure of tangential discontinuities (TDs) in collisionless plasmas. This paper reviews kinetic models based on steady-state solutions of the Vlasov equation. It is shown that most of the existing models are special cases of a generalized multi-species model. In this generalized model all particle populations from both outer regions and from inside the layer - are described using a unique formalism for the velocity distribution functions. Because of their historical importance, the Harris and Sestero models are reviewed and deduced from the generalized model. The Lee and Kan model is also a special case of the generalized model. The generalized model, however, is also able to describe TDs with velocity shear and large angles of magnetic field rotation. Such a multi-species model with a large number of free parameters and different gradient scales illustrates many observable features of TDs, including their multiscale fine structure. Particular attention is paid to the magnetopause. Observed magnetopause crossings are simulated. The effects of the relative flow velocity and asymmetrical magnetic field profiles on the structure of the magnetopause and on its stability with respect to tearing perturbations are discussed. We also present calculations that demonstrate the potential of the generalized model in explaining the origin of discrete auroral arcs. Numerical simulations of solar wind TDs with heavy ions and a large spectrum of thicknesses are also feasible. This indicates that such a model is of fundamental importance for understanding the detailed structure of solar wind TDs, like those observed by the interplanetary spacecraft ULYSSES. The problems associated with the one-dimensional, time-independent Vlasov approach are discussed and a variational principle is suggested to reduce the arbitrariness resulting from the large number of free parameters.