The objective of this paper is to examine trace forms and representations of finite-dimensional evolution algebras. On the one hand, we give a necessary and sufficient condition for a finite-dimensional evolution algebra to admit a non-degenerate trace form. We illustrate this condition with examples on evolution algebras of dimension 2 defined up to isomorphism. We provide a necessary and sufficient condition for a finite-dimensional evolution algebra admitting a non-degenerate trace form to be a baric algebra. On the other hand, we show that a finite-dimensional evolution algebra does not, in general, admit a non-trivial representation. For finite-dimensional degenerate evolution algebras, we exhibit a non-trivial representation and prove that the irreducible submodules of this representation are of dimension one. Moreover, we present a necessary and sufficient condition for this representation to be associative.