Modern option pricing techniques are often considered among the most mathematically complex of all applied areas of finance. Financial analysts have reached the point where they are able to calculate, with alarming accuracy, the value of a stock option. Most of the models and techniques employeed by today's analysts are rooted in a model developed by Fischer Black and Myron Scholes in 1973. This paper examines the evolution of option pricing models leading up to and beyond Black and Scholes' model.