The identification of drug-target interactions (DTIs) is a key task in drug discovery, where drugs are chemical compounds and targets are proteins.  Traditional DTI prediction methods are either time consuming (simulation-based methods) or heavily dependent on domain expertise (similarity-based and feature-based methods). In this work, we propose an end-to-end neural network model that predicts DTIs directly from low level representations.  In addition to making predictions, our model provides biological interpretation using two-way attention mechanism. Instead of using simplified settings where a dataset is evaluated as a whole, we designed an evaluation dataset from BindingDB following more realistic settings where predictions of unobserved examples (proteins and drugs) have to be made.  We experimentally compared our model with matrix factorization, similarity-based methods, and a previous deep learning approach.  Overall, the results show that our model outperforms other approaches without requiring domain knowledge and feature engineering.  In a case study, we illustrated the ability of our approach to provide biological insights to interpret the predictions.