We develop a model of firm dynamics through product innovation that explicitly incorporates advertising decisions by firms. We model advertising by constructing a framework that unifies a number of facts identified by the empirical marketing literature. The model is then used to explain several empirical regularities across firm sizes using U.S. data. Through a novel interaction between R&D and advertising, we are able to explain empirically observed deviations from Gibrat's law, as well as the behavior of advertising expenditures across firms, the degree of substitution between R&D and advertising expenditures as firms grow large, and broadly the effects of advertising on both firm and economic growth. We find that smaller firms can be both more innovation-and advertising-intensive as in the data even when there exist increasing returns to scale in research.