A landmark result by Dykema in 1993 classified free products of finite-dimensional von Neumann algebras equipped with tracial states. In 1997, Shlyakhtenko constructed the almost periodic free Araki-Woods factors, a natural non-tracial analogue to free group factors. He asked whether free products of finite-dimensional von Neumann algebras with respect to non-tracial states can be described in terms of free Araki-Woods factors. In this talk, I will answer Shlyakhtenko's question in the affirmative, therefore providing a complete classification of free products of finite dimensional von Neumann algebras. This is joint work with Brent Nelson.