  We revisit the existence, background independence and uniqueness of closed,
open and open-closed bosonic- and topological string field theory, using the
machinery of homotopy algebra. In a theory of classical open- and closed
strings, the space of inequivalent open string field theories is isomorphic to
the space of classical closed string backgrounds. We then discuss obstructions
of these moduli spaces at the quantum level. For the quantum theory of closed
strings, uniqueness on a given background follows from the decomposition
theorem for loop homotopy algebras. We also address the question of background
independence of closed string field theory.
