Neural dialog models have exhibited strong performance, however their end-to-end nature lacks a representation of the explicit structure of dialog. This results in a loss of generalizability, controllability and a data-hungry nature. Conversely, more traditional dialog systems do have strong models of explicit structure. This paper introduces several approaches for explicitly incorporating structure into neural models of dialog. Structured Fusion Networks first learn neural dialog modules corresponding to the structured components of traditional dialog systems and then incorporate these modules in a higher-level generative model. Structured Fusion Networks obtain strong results on the MultiWOZ dataset, both with and without reinforcement learning. Structured Fusion Networks are shown to have several valuable properties, including better domain generalizability, improved performance in reduced data scenarios and robustness to divergence during reinforcement learning.