For almost two centuries the whole electronics was based on three fundamental elements: resistor, capacitor, and inductor. In 1971, Leon Chua theorized about a fourth fundamental circuit element termed 'Memristor' that was implemented for the first time by Stanley Williams and co-workers at HP Labs, in 2008. The Memristor behaves as a variable resistor capable of remembering its last resistance value after the polarization is removed, like a non-volatile memory. Due to its properties, the memristor has become an important topic under study in several areas such: as non-volatile memories, neural networks and logical circuits. This paper presents an overview of the state of the art of theory, models, circuits, and applications of the memristor, providing a simple academic approach to students who do not necessarily have had courses of quantum mechanics or similar ones.