As recognized by a recent Nobel Prize in Economics, the Black-Scholes-Merton formula for options pricing irreversibly transformed Wall Street in 1973. Almost overnight, the intuitive art of trading was replaced by the quantitative science of stochastic processes. In the past decade or two, however, various assumptions behind the model have been systematically violated, sometimes with disastrous effects (e.g. the 1987 crash). In this lecture, the basic elements of a more general theory of pricing and hedging stock options and other so-called "financial derivatives" is presented, which serves to illustrate an emerging shift from the Black-Scholes-Merton way of thinking to account for real financial risk. This paradigm shift is being driven by the recent flux of ideas (and also of people!) from theoretical physics to finance.