The dependence of the current-voltage curve on voltage sweep direction, sweep rate, and the situation (pre-bias, illumination) a CH3NH3PbI3 perovskite solar cell has faced before a scan, makes a simple determination of the efficiency more difficult and results in what is called a rate-dependent hysteresis in the current-voltage relation. In this work we show that the rate-dependent hysteresis is related to a slow field-induced process that tends to cancel the electric field in the device at each applied bias voltage. It is attributed to the built-up of space charge close to the contacts, independent of illumination and most likely due to ionic movement, which is enhanced when the device undergoes aging. This process can also lead to a reduction of the steady-state photocurrent and does not directly correlate with the development of the hysteresis if it is measured at a fixed voltage sweep rate. Consequently, investigating the hysteresis itself at a given voltage sweep rate is not sufficient to understand the effects causing the hysteresis. We show that the difference between the photocurrent when scanning from positive to negative bias and the other way around is not related to a displacement current, but to a modified charge-carrier collection efficiency. Our experimental approach allows to discriminate between slow and fast processes, where we compare planar architectures with devices based on a mesoscopic scaffold. We apply a device model to assist the analysis of the experimental data.