Compositionality is useful to reduce the complexity of machine learning models and increase their generalization capabilities, because new problems can be linked to the composition of existing solutions. Recent work has shown that compositional approaches can offer substantial benefits over a wide variety of tasks, from multi-task learning over visual question-answering to natural language inference, among others. A key variant is functional compositionality, where a meta-learner composes different (trainable) functions into complex machine learning models. In this thesis, I generalize existing approaches to functional compositionality under the umbrella of the routing paradigm, where trainable arbitrary functions are 'stacked' to form complex machine learning models.