The auroral zone ionosphere is coupled to the outer magnetosphere by means of field-aligned currents. Parallel electric fields associated with these currents are now widely accepted to be responsible for the acceleration of auroral particles. This paper will review the theoretical concepts and models describing this coupling. The dynamics of auroral zone particles will be described, beginning with the adiabatic motions of particles in the converging geomagnetic field in the presence of parallel potential drops and then considering the modifications to these adiabatic trajectories due to wave-particle interactions. The formation of parallel electric fields can be viewed both from microscopic and macroscopic viewpoints. The presence of a current carrying plasma can give rise to plasma instabilities which in a weakly turbulent situation can affect the particle motions, giving rise to an effective resistivity in the plasma. Recent satellite observations, however, indicate that the parallel electric field is organized into discrete potential jumps, known as double layers. From a macroscopic viewpoint, the response of the particles to a parallel potential drop leads to an approximately linear relationship between the current density and the potential drop. The currents flowing in the auroral circuit must close in the ionosphere. To a first approximation, the ionospheric conductivity can be considered to be constant, and in this case combining the ionospheric Ohm's Law with the linear current-voltage relation for parallel currents leads to an outer scale length, above which electric fields can map down to the ionosphere and below which parallel electric fields become important. The effects of particle precipitation make the picture more complex, leading to enhanced ionization in upward current regions and to the possibility of feedback interactions with the magnetosphere. Determining adiabatic particle orbits in steady-state electric and magnetic fields can be used to determine the self-consistent particle and field distributions on auroral field lines. However, it is difficult to pursue this approach when the fields are varying with time. Magnetohydrodynamic (MHD) models deal with these time-dependent situations by treating the particles as a fluid. This class of model, however, cannot treat kinetic effects in detail. Such effects can in some cases be modeled by effective transport coefficients inserted into the MHD equations. Intrinsically time-dependent processes such as the development of magnetic micropulsations and the response of the magnetosphere to ionospheric fluctuations can be readily treated in this framework. The response of the lower altitude auroral zone depends in part on how the system is driven. Currents are generated in the outer parts of the magnetosphere as a result of the plasma convection. The dynamics of this region is in turn affected by the coupling to the ionosphere. Since dissipation rates are very low in the outer magnetosphere, the convection may become turbulent, implying that nonlinear effects such as spectral transfer of energy to different scales become important. MHD turbulence theory, modified by the ionospheric coupling, can describe the dynamics of the boundary-layer region. Turbulent MHD fluids can give rise to the generation of field-aligned currents through the so-called α-effect, which is utilized in the theory of the generation of the Earth's magnetic field. It is suggested that similar processes acting in the boundary-layer plasma may be ultimately responsible for the generation of auroral currents.