The article discusses the fundamental properties and characteristics of memristors, which are 2-terminal non-volatile memory devices that exhibit a distinctive "fingerprint" known as a pinched hysteresis loop in the $v-i$ plane. The author emphasizes that this fingerprint is a defining feature of memristors, regardless of the material or physical mechanism used. The article provides a detailed mathematical derivation of the memristor's constitutive relation and its associated memristance and memductance, and explains how these properties lead to the unique hysteresis loop behavior. It also explores the concept of the resistance vs. state map, which is a graphical representation of the memristor's behavior, and discusses the importance of distinguishing between resistance and resistor in nonlinear devices. The article further examines the relationship between small-signal and chord memristance, and introduces the idea of unfolding the memristor to develop more precise models of non-volatile resistance switching memory devices. Finally, it presents examples of various memristor models and their applications in different materials and physical mechanisms, highlighting the versatility and potential of memristors in digital and analog circuit design.The article discusses the fundamental properties and characteristics of memristors, which are 2-terminal non-volatile memory devices that exhibit a distinctive "fingerprint" known as a pinched hysteresis loop in the $v-i$ plane. The author emphasizes that this fingerprint is a defining feature of memristors, regardless of the material or physical mechanism used. The article provides a detailed mathematical derivation of the memristor's constitutive relation and its associated memristance and memductance, and explains how these properties lead to the unique hysteresis loop behavior. It also explores the concept of the resistance vs. state map, which is a graphical representation of the memristor's behavior, and discusses the importance of distinguishing between resistance and resistor in nonlinear devices. The article further examines the relationship between small-signal and chord memristance, and introduces the idea of unfolding the memristor to develop more precise models of non-volatile resistance switching memory devices. Finally, it presents examples of various memristor models and their applications in different materials and physical mechanisms, highlighting the versatility and potential of memristors in digital and analog circuit design.