  The theory of Leavitt path algebras is intrinsically related, via graphs, to
the theory of symbolic dynamics and $C^*$-algebras where the major
classification programs have been a domain of intense research in the last 50
years. In this survey article, we gather together current lines of research in
the classification of Leavitt path algebras, questions, conjectures, and some
of the results about them that have been obtained so far.
