The application of Deep Neural Networks for ranking in search engines may obviate the need for the extensive feature engineering common to current learning-to-rank methods. However, we show that combining simple relevance matching features like BM25 with existing Deep Neural Net models often substantially improves the accuracy of these models, indicating that they do not capture essential local relevance matching signals. We describe a novel deep Recurrent Neural Net-based model that we call Match-Tensor. The architecture of the Match-Tensor model simultaneously accounts for both local relevance matching and global topicality signals allowing for a rich interplay between them when computing the relevance of a document to a query. On a large held-out test set consisting of social media documents, we demonstrate not only that Match-Tensor outperforms BM25 and other classes of DNNs but also that it largely subsumes signals present in these models.