With conventional CMOS technologies approaching their scaling limits, researchers are actively investigating alternative technologies for ever increasing computing and mobile demand. A number of different technologies are currently being studied by different research groups. In the last decade, one-dimensional (1D) carbon nanotubes (CNT), graphene, which is a two-dimensional (2D) natural occurring carbon rolled in tubular form, and zero-dimensional (0D) fullerenes have been the subject of intensive research. In 2008, HP Labs announced a ground-breaking fabrication of memristors, the fourth fundamental element postulated by Chua at the University of California, Berkeley in 1971. In the last few years, the memristor has gained a lot of attention from the research community. In-depth studies of the memristor and its analog behavior have convinced the community that it has the potential in future nano-architectures for optimization of high-density memory and neuromorphic computing architectures. The objective of this thesis is to explore memristors for analog and mixed-signal system design using Simscape. This thesis presents a memristor model in the Simscape language. Simscape has been used as it has the potential for modeling large systems. A memristor based programmable oscillator is also presented with simulation results and characterization. In addition, simulation results of different memristor models …