Neural networks are a powerful model class to learn machine Reading Comprehen- sion (RC), yet they crucially depend on the availability of suitable training datasets. In this thesis we describe methods for data collection, evaluate the performance of established models, and examine a number of model behaviours and dataset limita- tions. We first describe the creation of a data resource for the science exam QA do- main, and compare existing models on the resulting dataset. The collected ques- tions are plausible – non-experts can distinguish them from real exam questions with 55% accuracy – and using them as additional training data leads to improved model scores on real science exam questions. Second, we describe and apply a distant supervision dataset construction method for multi-hop RC across documents. We identify and mitigate several dataset assembly pitfalls – a lack of unanswerable candidates, label imbalance, and spurious correlations between documents and particular candidates – which often leave shallow predictive cues for the answer. Furthermore we demonstrate that se- lecting relevant document combinations is a critical performance bottleneck on the datasets created. We thus investigate Pseudo-Relevance Feedback, which leads to improvements compared to TF-IDF-based document combination selection both in retrieval metrics and answer accuracy. Third, we investigate model undersensitivity: model predictions do not change when given adversarially altered questions in SQUAD2.0 and NEWSQA, even though they should. We characterise affected samples, and show that the phe- nomenon is related to a lack of structurally similar but unanswerable samples during training: data augmentation reduces the adversarial error rate, e.g. from 51.7% to 20.7% for a BERT model on SQUAD2.0, and improves robustness also in other settings. Finally we explore efficient formal model verification via Interval Bound Propagation (IBP) to measure and address model undersensitivity, and show that using an IBP-derived auxiliary loss can improve verification rates, e.g. from 2.8% to 18.4% on the SNLI test set.