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Within the fully integrated magnetosphere-ionosphere system, many electrodynamic processes interact with each other. We review recent advances in understanding three major meso-scale coupling processes within the system: the transient field-aligned currents (FACs), mid-latitude plasma convection, and auroral particle precipitation. (1) Transient FACs arise due to disturbances from either dayside or nightside magnetosphere. As the interplanetary shocks suddenly compress the dayside magnetosphere, short-lived FACs are induced at high latitudes with their polarity successively changing. Magnetotail dynamics, such as substorm injections, can also disturb the current structures, leading to the formation of substorm current wedges and ring current disruption. (2) The mid-latitude plasma convection is closely associated with electric fields in the system. Recent studies have unraveled some important features and mechanisms of subauroral fast flows. (3) Charged particles, while drifting around the Earth, often experience precipitating loss down to the upper atmosphere, enhancing the auroral conductivity. Recent studies have been devoted to developing more self-consistent geospace circulation models by including a better representation of the auroral conductance. It is expected that including these new advances in geospace circulation models could promisingly strengthen their forecasting capability in space weather applications. The remaining challenges especially in the global modeling of the circulation system are also discussed.