Dynamical systems based on transformations of measure spaces were a natural mathematical abstraction from statistical mechanics in the early years of last century. The theory was developed by Kolmogorov and Sinai, and Shannon applied it to information theory. The notion of entropy is key in understanding how chaotic these systems are. I shall give a survey of the theory of entropy and some recent results on structure of dynamical systems and entropy for non-singular systems. Some of this has applications to new areas, and I have talked to DSTO about modelling battlefields using it.