  We study representations of a Leavitt path algebra $L$ of a finitely
separated digraph $\Gamma$ over a field. We show that the category of
$L$-modules is equivalent to a full subcategory of quiver representations. When
$\Gamma$ is a (non-separated) row-finite digraph we determine all possible
finite dimensional quotients of $L$ after giving a necessary and sufficient
graph theoretic criterion for the existence of a nonzero finite dimensional
quotient. This criterion is also equivalent to $L$ having UGN (Unbounded
Generating Number) as well as being algebraically amenable. We also realize the
category of $L$-modules as a retract, hence a quotient by an explicit Serre
subcategory of the category of quiver representations (that is,
$\mathbb{F}\Gamma$-modules) via a new colimit model for
$M\otimes_{\mathbb{F}\Gamma} L$.
