Resistive‐switching random‐access memory (RRAM) based on ion migration in insulating layers might revolutionize future nanoelectronic circuits for both memory and logic. The high‐speed, low‐power change of resistance in RRAM can be exploited not only for data storage but also for reconfiguration of programmable logic circuits and for neuromorphic computation. In this review, the strengths and limitations of RRAM will be discussed. First, the RRAM concept will be reviewed in terms of memory operation and physical mechanisms for switching. The RRAM architectures will be discussed with emphasis on the crossbar array structure allowing for high density and reliable operation through proper selector devices. Finally, the RRAM applications in computing systems will be reviewed, addressing the RRAM switch in field‐programmable gate array (FPGA) and neuromorphic circuits.