$L_{\infty}$ algebras are natural generalizations of Lie algebras from a homotopy theoretical point of view. Representations of these structures are robust in nature and have yet to be explored in depth. We will briefly review the expository work of Lada and Markl on $L_{\infty}$ algebra representations, then will explore homomorphisms of $L_{\infty}$ modules. We will also discuss an example of a finite dimensional $L_{\infty}$ module.