Technologies relating to implementing memristor crossbar arrays using non-filamentary RRAM cells are disclosed. In some implementations, an apparatus comprises: a first row wire; a first column wire; a non-filamentary RRAM; and an access control device. The non-filamentary RRAM and the access control device are serially connected; the non-filamentary RRAM and the access control device connect the first row wire with the first column wire. The non-filamentary RRAM and the access control device may form a cross-point device. The cross-point device may be less than 40×40 nm2. A set current of the non-filamentary RRAM may be no more than 10 μA; and a reset current of the non-filamentary RRAM is no more than 10 μA. The access control device may comprise a transistor or a selector.