In this chapter, we will discuss mathematical models of the master circadian rhythm in the suprachiasmatic nucleus of the hypothalamus with a particular emphasis on models that incorporate the effect of light on circadian phase resetting and melatonin suppression. We will show that limit cycle oscillators provide a better representation of the salient properties of the human circadian system than a sinusoid. We will then discuss how the phototransduction of light to the SCN has been incorporated in various models. Finally, we will introduce different theoretical and practical applications of these models and highlight areas for future model development.