In this paper I will try to describe how the theory of stochastic processes and especially of stochastic differential equations has influenced option pricing theory. In my view, this is one of the best examples of the application of sophisticated mathematics to a purely economic, or financial, problem. This is not only because of the fact that the theory describes the economic phenomena very well, but merely since the main results are used in every day practice by market makers. I will discuss the pricing of options on stocks and bonds and mention some other examples.