Neural IR models, such as DRMM and PACRR, have achieved strong results by successfully capturing relevance matching signals. We argue that the context of these matching signals is also important. Intuitively, when extracting, modeling, and combining matching signals, one would like to consider the surrounding text (local context) as well as other signals from the same document that can contribute to the overall relevance score. In this work, we highlight three potential shortcomings caused by not considering context information and propose three neural ingredients to address them: a disambiguation component, cascade k-max pooling, and a shuffling combination layer. Incorporating these components into the PACRR model yields Co-PACRR, a novel context-aware neural IR model. Extensive comparisons with established models on Trec Web Track data confirm that the proposed model can achieve superior search results. In addition, an ablation analysis is conducted to gain insights into the impact of and interactions between different components. We release our code to enable future comparisons.