This thesis is about representations of Leavitt Path Algebras (LPAs). Specifically, we first generalize a previously known construction of twisted Chen modules over the Leavitt Path Algebra of a directed graph. We then give some thought to its extension to other modules, and present new classes of simple Leavitt Path Algebra modules previously unknown. These are modules generated by indicator functions of closed sets of the set of all infinite paths of a directed graph.