We review the latest developments in computational methods for direct simulation of fully fluctuating field theories of polymeric assemblies. In this context, we describe a newly developed theoretical and computational framework for accurately computing fluctuation-corrected phase diagrams of mesostructured polymer systems and report the first such complete phase diagram for a diblock copolymer melt. The method is based on complex Langevin sampling of a UV regularized field-theoretic model, with Helmholtz free energies computed using thermodynamic integration. UV regularization ensures that the free energies do not have an arbitrary reference; they can be compared between incommensurate phases, permitting for the first time the computation of order–order transitions with fluctuation corrections. We further demonstrate that computed free energies are accurate in the disordered phase by comparison to perturbation theory on the one-loop level. Importantly, we note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt or solution. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures.