Repeats of short patterns such as CACACA... appear in our DNA at a frequency far greater than if they were due to chance. These repeats have a high mutation rate compared to nucleotide substitutions, so they are useful for locating genes and for understanding population structure on the scale of thousands of years. In this talk we will describe a simple model of the evolution of these repeat sequences developed in joint work with Semyon Kruglyak, Malcolm Schug, and Chip Aquadro, and we will fit this model to DNA sequence data from yeast, fruit flies, mice, and humans. The model fits the observed data and gives parameter estimates that are consistent with experimental work.