We review recent theoretical progress in understanding the origins of the jovian main auroral oval emissions, based on the hypothesis that they are connected with the magnetosphere-ionosphere coupling current circuit which maintains plasma corotation in the middle magnetosphere. After the development of the basic theory, we compare results obtained with differing models of the background magnetic field, showing that an appropriate choice is crucial in determining the strength, width, and location of the precipitating auroral electron energy flux associated with the region of upward field-aligned current. Specific comparison is made between results for a dipole field and an empirically based current sheet model, in which the angular velocity profile of the plasma is calculated self-consistently using Hill-Pontius theory. We also develop simple approximation regimes appropriate to small and large equatorial distances, showing that the currents depend on the mass outflow rate of iogenic plasma and not on the effective ionospheric Pedersen conductivity in the small-distance regime, and vice versa at large distances. We also discuss the expected anticorrelation of the auroral emission intensity with solar wind dynamic pressure and present steady state results representing differing degrees of magnetospheric compression. Significant modulation of the emission is anticipated on this basis.