The theory of vertex operator algebras (VOAs) is relatively recent and has deep roots and applications in physics and mathematics, for example the explanation of "monstrous moonshine". Our focus is on the mathematical side, and more precisely the algebras arising from VOAs. A recent important development is that the structure of algebras arising from OZ VOAs has been axiomatized. This gives rise to so-called axial algebras and more generally decomposition algebras. The goal of this research is to study the algebras arising from VOAs in the context of (axial) decomposition algebras. Our main objective will be to investigate how the theory of VOAs can lead towards answers in the theory of decomposition algebras. We will study three major themes. 1. Representations and modules: we study how the methods of defining representations and modules of VOAs can give insights in defining them for (axial) decomposition algebras; 2. Interplay between OZ-VOAs and (axial) decomposition algebras; 3. Non-commutative algebra products from VOAs: recently, an explicit construction was found of a certain 3875-dimensional algebra, invariant under the linear algebraic group of type E8. The current construction is quite involved, and very much "ad hoc", whereas in my master thesis I found an interpretation inside a VOA, constructed from a Lie algebra. This method, which is much more natural, has potentially a large impact.