Results on controllability, observability and realization of input/output data for linear systems are well-known and extensively covered in a variety of books and papers. What is not so well-known is that substantial progress has been made in recent years on providing similarly detailed results for nonlinear processes. This paper represents a survey of the most interesting work on nonlinear systems, together with a discussion of the major obstacles standing in the way of a comprehensive theory of nonlinear systems.