Methylammonium lead iodide (MAPI) cells of the design FTO/sTiO(2)/mpTiO(2)/MAPI/Spiro-OMeTAD/Au, where FTO is fluorine-doped tin oxide, sTiO(2) indicates solid-TiO2, and mpTiO(2) is mesoporous TiO2, are studied using transient photovoltage (TPV), differential capacitance, charge extraction, current interrupt, and chronophotoamperometry. We show that in mpTiO(2)/MAPI cells there are two kinds of extractable charge stored under operation: a capacitive electronic charge (similar to 0.2 mu C/cm(2)) and another, larger charge (40 mu C/cm(2)), possibly related to mobile ions. Transient photovoltage decays are strongly double exponential with two time constants that differ by a factor of similar to 5, independent of bias light intensity. The fast decay (similar to 1 mu s at 1 sun) is assigned to the predominant charge recombination pathway in the cell. We examine and reject the possibility that the fast decay is due to ferroelectric relaxation or to the bulk photovoltaic effect. Like many MAPI solar cells, the studied cells show significant JV hysteresis. Capacitance vs open circuit voltage (V-oc) data indicate that the hysteresis involves a change in internal potential gradients, likely a shift in band offset at the TiO2/MAPI interface. The TPV results show that the Voc hysteresis is not due to a change in recombination rate constant. Calculation of recombination flux at V-oc suggests that the hysteresis is also not due to an increase in charge separation efficiency and that charge generation is not a function of applied bias. We also show that the JV hysteresis is not a light driven effect but is caused by exposure to electrical bias, light or dark.