Perhaps you’ve heard of a Markov chain, but have you heard of a martingale? In this presentation we will explore this specific type of stochastic process by reviewing a number of interesting examples - including some related to gambling-as well as establishing some properties of martingales. We will also explore some relevant theorems, including the Maximal Inequality Theorem for nonnegative martingales, and the Optional Stopping Theorem. We will also certainly examine some interesting consequences of these results in context.