For a field K, the Leavitt path algebra over a directed graph was introduced by G. Abrams and G. A. Pino (2005) and P. Ara, M.A. Moreno, and E. Pardo (2007). Recently there has been significant interest generalizing the construction of Leavitt path algebras by replacing the field with a commutative unital ring . The purpose of this talk is to define Leavitt path algebras, describe some of their fundamental properties and mention a few recent developments in this area.