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The memristor has been proposed as the fourth circuit element. Among the emerging nano-technologies, the memristor has become a very promising candidate for building storage structures because of its shorter switching time, higher capacity and lower power consumption. In this thesis, I will first introduce a new memristor model with controllable window functions, which is more authentic and flexible than those existing memristor models. Then I will present my novel design of a Memristor Content Addressable Memory (Memristor-CAM) structure that is based on my own design of Memristor-CAM cells. The major contribution of this work is the fuzzy look-up functionality, which is achieved by summing up the current of the matched cell lines in the Memristor-CAM. In addition, this fuzzy look-up functionality of the new Memristor-CAM design could be further extended in order to fit into a lot of practical applications. With the benefits of memristors, this Memristor-CAM storage structure could reduce the power consumption, increase the capacity and improve the performance of computer memory. My new design is tested in a common experimental design that includes computer simulations and circuit emulations. The results of my experiments support the validity of my contributions and allow further analysis and insights on the behaviours of memristors when different settings are applied.