The memristor is the fundamental non-linear circuit element, with uses in\ncomputing and computer memory. ReRAM (Resistive Random Access Memory) is a\nresistive switching memory proposed as a non-volatile memory. In this review we\nshall summarise the state of the art for these closely-related fields,\nconcentrating on titanium dioxide, the well-utilised and archetypal material\nfor both. We shall cover material properties, switching mechanisms and models\nto demonstrate what ReRAM and memristor scientists can learn from each other\nand examine the outlook for these technologies.\n