Circuit or electronic components are useful elements allowing the realization of different circuit functionalities. The resistor, capacitor and inductor represent the three commonly known basic passive circuit elements owing to their fundamental nature relating them to the four circuit variables, namely voltage, magnetic flux, current and electric charge. The memory resistor (or memristor) was claimed to be the fourth basic passive circuit element, complementing the resistor, capacitor and inductor. This paper presents a review on the four basic passive circuit elements. After a brief recall on the first three known basic passive circuit elements, a thorough description of the memristor follows. Memristor sparks interest in the scientific community due to its interesting features, for example nano-scalability, memory capability, conductance modulation, connection flexibility and compatibility with CMOS technology, etc. These features among many others are currently in high demand on an industrial scale. For this reason, thousands of memristor-based applications are reported. Hence, the paper presents an in-depth overview of the philosophical argumentations of memristor, technologies and applications.