In 1948 Claude Shannon introduced the concept of information entropy to describe the information content of a signal.  Shannon's formulation of entropy and information theory has been widely developed in mathematics, physics, and computer science.  For example, in 1958 Kolmogorov defined the entropy of a dynamical system.  We will discuss the application of entropy to information theory and dynamical systems, and we will attempt to ferret out the relationship between entropy and the “complexity” of a system.