Hybrid Perovskites have emerged as a class of highly versatile functional materials with applications in solar cells, photodetectors, transistors, and lasers. Recently, there have also been reports on perovskite-based resistive switching (RS) memories, but there remain open questions regarding device stability and switching mechanism. Here, an RS memory based on a high-quality capacitor structure made of an MAPbBr3 (CH3NH3PbBr3) perovskite layer sandwiched between Au and indium tin oxide (ITO) electrodes is reported. Such perovskite devices exhibit reliable RS with an ON/OFF ratio greater than 103, endurance over 103 cycles, and a retention time of 104 s. The analysis suggests that the RS operation hinges on the migration of charged ions, most likely MA vacancies, which reversibly modifies the perovskite bulk transport and the Schottky barrier at the MAPbBr3/ITO interface. Such perovskite memory devices can also be fabricated on flexible polyethylene terephthalate substrates with high bendability and reliability. Furthermore, it is found that reference devices made of another hybrid perovskite MAPbI3 consistently exhibit filament-type switching behavior. This work elucidates the important role of processing-dependent defects in the charge transport of hybrid perovskites and provides insights on the ion-redistribution-based RS in perovskite memory devices.