Context-aware neural machine translation involves leveraging information beyond sentence-level context to resolve inter-sentential discourse dependencies and improve document-level translation quality, and has given rise to a number of recent techniques. However, despite well-reasoned intuitions, most context-aware translation models show only modest improvements over sentence-level systems. In this work, we investigate several challenges that impede progress within this field, relating to discourse phenomena, context usage, model architectures, and document-level evaluation. To address these problems, we propose a more realistic setting for document-level translation, called paragraph-to-paragraph (para2para) translation, and collect a new dataset of Chinese-English novels to promote future research.