The classical approach to comprehending complicated behavior in discretedynamical systems is Symbolic Dynamics. It seeks to replace intangiblecombinatorics of chaotic orbits by a set (a language) of infinite wordsover a finite alphabet.After giving a gentle introduction to the subject, we will discuss some veryrecent developments.Specifically, we will indicate how the algebraic topology of the Conley indexapplied to the phase space of the dynamical system leads to a new class of languages.The key issues, that are only partially resolved, are the algebraic understandingof random matrix products, and the functional analysis of certain new infinitedimensional transfer operators.Colorful handwritten transparencies will be used.