Charge accumulation at the electron and hole transport layers generates anomalous electrical behavior in perovskite solar cells (PSCs). Hysteresis in the current–voltage characteristic and recombination at the interfaces are the clearest manifestations of this phenomenon, which compromises device performance and stability. Here, the underlying charge-carrier dynamics of a variety of PSCs are investigated by analyzing their transient photocurrent response. Towards shorter time scales, PSCs often show increasingly severe hysteretic responses. This phenomenon is correlated with the presence of interfacial accumulated charges that hinders the photogenerated carrier extraction process. However, introducing passivating contacts improves the carrier-injection properties and the devices become completely hysteresis free. These results underline the importance of contact passivation for PSCs and the need to further develop new passivating interlayers that simultaneously eliminate charge-carrier recombination and provide selective transport for each carrier type at the PSC's contacts.