Recurrent neural network grammars (RNNG) are a recently proposed probabilistic generative modeling family for natural language. They show state-of-the-art language modeling and parsing performance. We investigate what information they learn, from a linguistic perspective, through various ablations to the model and the data, and by augmenting the model with an attention mechanism (GA-RNNG) to enable closer inspection. We find that explicit modeling of composition is crucial for achieving the best performance. Through the attention mechanism, we find that headedness plays a central role in phrasal representation (with the model's latent attention largely agreeing with predictions made by hand-crafted head rules, albeit with some important differences). By training grammars without nonterminal labels, we find that phrasal representations depend minimally on nonterminals, providing support for the endocentricity hypothesis.