We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this line restricts data to follow a hierarchical tree structure and thus lacks inter-span communications.To overcome the problem, we propose a novel contextual inside-outside (CIO) layer that learns contextualized representations of spans through bottom-up and top-down passes, where a bottom-up pass forms representations of high-level spans by composing low-level spans, while a top-down pass combines information inside and outside a span. By stacking several CIO layers between the embedding layer and the attention layers in Transformer, the ReCAT model can perform both deep intra-span and deep inter-span interactions, and thus generate multi-grained representations fully contextualized with other spans.Moreover, the CIO layers can be jointly pre-trained with Transformers, making ReCAT enjoy scaling ability, strong performance, and interpretability at the same time. We conduct experiments on various sentence-level and span-level tasks. Evaluation results indicate that ReCAT can significantly outperform vanilla Transformer models on all span-level tasks and recursive models on natural language inference tasks. More interestingly, the hierarchical structures induced by ReCAT exhibit strong consistency with human-annotated syntactic trees, indicating good interpretability brought by the CIO layers.