Deep learning based techniques have been recently used with promising results for data integration problems. Some methods directly use pre-trained embeddings that were trained on a large corpus such as Wikipedia. However, they may not always be an appropriate choice for enterprise datasets with custom vocabulary. Other methods adapt techniques from natural language processing to obtain embeddings for the enterprise's relational data. However, this approach blindly treats a tuple as a sentence, thus losing a large amount of contextual information present in the tuple. We propose algorithms for obtaining local embeddings that are effective for data integration tasks on relational databases. We make four major contributions. First, we describe a compact graph-based representation that allows the specification of a rich set of relationships inherent in the relational world. Second, we propose how to derive sentences from such a graph that effectively "describe" the similarity across elements (tokens, attributes, rows) in the two datasets. The embeddings are learned based on such sentences. Third, we propose effective optimization to improve the quality of the learned embeddings and the performance of integration tasks. Finally, we propose a diverse collection of criteria to evaluate relational embeddings and perform an extensive set of experiments validating them against multiple baseline methods. Our experiments show that our framework, EmbDI, produces meaningful results for data integration tasks such as schema matching and entity resolution both in supervised and unsupervised settings.