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Perovskite-based photovoltaics have been rapidly developed, with record power conversion efficiencies now exceeding 22%. In order to rationally design efficient and stable perovskite solar cells, it is important to understand not only charge trapping and recombination events, but also processes occurring at the perovskite/transport material (TM) interface, such as charge transfer and interfacial recombination. In this work, time-resolved microwave conductivity measurements are performed to investigate these interfacial processes for methylammonium lead iodide and various state-of-the-art organic TMs. A global kinetic model is developed, which accurately describes both the dynamics of excess charges in the perovskite layer and transfer to charge-specific TMs. The authors conclude that for state-of-the-art materials, such as Spiro-OMeTAD and PCBM, the charge extraction efficiency is not significantly affected by intra-band gap traps for trap densities under 1015 cm-3. Finally, the transfer rates to C60, PCBM, EDOT-OMeTPA, and Spiro-OMeTAD are sufficient to outcompete second order recombination under excitation densities representative for illumination by AM1.5. [ABSTRACT FROM AUTHOR]