Classification conjectures for Leavitt path algebras

The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and $C^{\ast }$-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.