I will report on the story of associating C*-algebras to symbolic dynamical systems such as directed graphs, and the recently articulated program of understanding dynamical relations (such as conjugacy or flow equivalence) in terms of structure-preserving *-isomorphisms of the corresponding C*-algebras. A large body of rigidity results have successfully been obtained for graphs and more general systems. There will be an emphasis on open questions and problems yet to be solved!