  Log-symplectic structures are Poisson structures that are determined by a
symplectic form with logarithmic singularities. We construct moduli spaces of
curves with values in a log-symplectic manifold. Among the applications, we
classify symplectically ruled log-symplectic $4$ manifolds (both orientable and
non-orientable), and obstruct the existence of contact boundary components, in
analogy with well-known theorems by McDuff. Moreover, we study certain
log-symplectically ruled surfaces, using tools from symplectic field theory.
