Field programmable gate arrays using resistivity-sensitive memories are described, including a programmable cell comprising a configurable logic, a memory connected to the configurable logic to provide functions for the configurable logic, the memory comprises a non-volatile rewriteable memory element including a resistivity-sensitive memory element, an input/output logic connected to the configurable logic and the memory to communicate with other cells. The memory elements may be two-terminal resistivity-sensitive memory elements that store data in the absence of power. The two-terminal memory elements may store data as plurality of conductivity profiles that can be non-destructively read by applying a read voltage across the terminals of the memory element and data can be written to the two-terminal memory elements by applying a write voltage across the terminals. The memory can be vertically configured in one or more memory planes that are vertically stacked upon each other and are positioned above a logic plane.