A memristor with a switching layer that includes a composite of multiple phases is disclosed. The memristor comprises: a first electrode; a second electrode spaced from the first electrode; and a switching layer positioned between the first electrode and the second electrode, the switching layer comprising the multi-phase composite system that comprises a first majority phase comprising a relatively insulating matrix of a switching material and a second minority phase comprising a relatively conducting material for forming at least one conducting channel in the switching layer during a fabrication process of the memristor. A method of making the memristor and a crossbar employing the memristor are also disclosed.