We introduce Recursive Routing Networks (RRNs), which are modular, adaptable models that learn effectively in diverse environments. RRNs consist of a set of functions, typically organized into a grid, and a meta-learner decision-making component called the router. The model jointly optimizes the parameters of the functions and the meta-learner's policy for routing inputs through those functions. RRNs can be incorporated into existing architectures in a number of ways; we explore adding them to word representation layers, recurrent network hidden layers, and classifier layers. Our evaluation task is natural language inference (NLI). Using the MULTINLI corpus, we show that an RRN's routing decisions reflect the high-level genre structure of that corpus. To show that RRNs can learn to specialize to more fine-grained semantic distinctions, we introduce a new corpus of NLI examples involving implicative predicates, and show that the model components become fine-tuned to the inferential signatures that are characteristic of these predicates.