Leon Chua introduced the concept that all 2-terminal non-volatile memory devices based on resistance switching are memristors, regardless of the material or physical mechanism. These devices exhibit a distinctive "pinched hysteresis loop" in the v-i plane, confined to the first and third quadrants, with a contour shape that changes with the amplitude and frequency of the input voltage or current. The loop shrinks and tends to a straight line as frequency increases. Examples of such loops have been observed in various fields, but the focus here is on solid-state and nano devices. The memristor is defined by a state-dependent Ohm's law, where the resistance depends on the device's past history. The memristor's behavior is characterized by a pinched hysteresis loop, which is a key fingerprint of the device. The memristor can be represented by a constitutive relation between charge and flux, and its resistance vs. state map allows for continuous tuning of resistance. The memristor's non-volatile memory property is due to its ability to retain state information even when power is removed. The paper also discusses the equivalence between the memristor's constitutive relation and its resistance vs. state map, and how the memristor can be used to model various resistance switching memories. The paper concludes that memristors can exhibit negative resistance in certain conditions, and that the concept of memristors can be extended to more complex systems through unfolding and morphing functions.Leon Chua introduced the concept that all 2-terminal non-volatile memory devices based on resistance switching are memristors, regardless of the material or physical mechanism. These devices exhibit a distinctive "pinched hysteresis loop" in the v-i plane, confined to the first and third quadrants, with a contour shape that changes with the amplitude and frequency of the input voltage or current. The loop shrinks and tends to a straight line as frequency increases. Examples of such loops have been observed in various fields, but the focus here is on solid-state and nano devices. The memristor is defined by a state-dependent Ohm's law, where the resistance depends on the device's past history. The memristor's behavior is characterized by a pinched hysteresis loop, which is a key fingerprint of the device. The memristor can be represented by a constitutive relation between charge and flux, and its resistance vs. state map allows for continuous tuning of resistance. The memristor's non-volatile memory property is due to its ability to retain state information even when power is removed. The paper also discusses the equivalence between the memristor's constitutive relation and its resistance vs. state map, and how the memristor can be used to model various resistance switching memories. The paper concludes that memristors can exhibit negative resistance in certain conditions, and that the concept of memristors can be extended to more complex systems through unfolding and morphing functions.