One of the defining characteristics of life is the ability to keep time, which organisms often achieve by using internal genetic "clocks" to govern fundamental cellular behavior. While the gene networks that produce oscillatory expression signals are typically quite elaborate, certain recurring network motifs are often found at the core of these biological clocks. In this lecture, I will describe our recent experimental and theoretical work on small genetic networks exhibiting oscillatory behavior. One common motif which may lead to oscillations is delayed auto-repression. We constructed synthetic oscillators based on this design principle, and observed robust and tunable oscillations both in bacteria and yeast. Since genetic systems typically involve small number of reacting components, intrinsic fluctuations play an important role in the dynamics. I will introduce theoretical and computational tools which can be used for modeling stochastic dynamics of small genetic networks.