Repeated multiplication of random variables can produce results that can be surprising at first encounter because there is no multiplicative analogue of the central limit theorem to provide intuition. In this talk, we will start by presenting some properties of products of random variables. We will then consider the  multiplicative analogue of the simple discrete random walk. For some choices of parameters, this process has the property that the expected value grows exponentially while every individual trajectory goes exponentially to zero with probability one. We will then look at a family of quasi-multiplicative random walks that interpolate in a sense between the additive and multiplicative cases in an attempt to understand where this behavior comes from. I will finish by discussing some applications of these models in economics and decision theory which tend to generate controversy in some quarters.