A multi-layer non-volatile memory integrally formed on top of a substrate including active circuitry is disclosed. Each layer of memory includes memory cells (e.g., a two-terminal memory cell) having a multi-resistive state material layer that changes its resistive state between a low resistive state and a high resistive state upon application of a write voltage across the memory cell. Data stored in the memory cells can be non-destructively determined by applying a read voltage across the memory cells. Data storage capacity can be tailored to a specific application by increasing or decreasing the number of memory layers that are integrally fabricated on top of the substrate (e.g., more than four layers or less than four layers). The memory cells can include a non-ohmic device for allowing access to the memory cell only during read and write operations. Each memory layer can comprise a cross point array.