We use coherence relations inspired by computational models of discourse to study the information needs and goals of image captioning. Using an annotation protocol specifically devised for capturing image--caption coherence relations, we annotate 10,000 instances from publicly-available image--caption pairs. We show that these coherence annotations can be exploited to learn relation classifiers as an intermediary step, and also train coherence-aware, controllable image captioning models. The results show a dramatic improvement in the consistency and quality of the generated captions with respect to information needs specified via coherence relations.