Relational triple extraction is challenging for its difficulty in capturing rich correlations between entities and relations. Existing works suffer from 1) heterogeneous representations of entities and relations, and 2) heterogeneous modeling of entity-entity interactions and entity-relation interactions. Therefore, the rich correlations are not fully exploited by existing works. In this paper, we propose UniRel to address these challenges. Specifically, we unify the representations of entities and relations by jointly encoding them within a concatenated natural language sequence, and unify the modeling of interactions with a proposed Interaction Map, which is built upon the off-the-shelf self-attention mechanism within any Transformer block. With comprehensive experiments on two popular relational triple extraction datasets, we demonstrate that UniRel is more effective and computationally efficient. The source code is available at https://github.com/wtangdev/UniRel.