Medical imaging is widely used in clinical practice for diagnosis and treatment. Report-writing can be error-prone for unexperienced physicians, and time- consuming and tedious for experienced physicians. To address these issues, we study the automatic generation of medical imaging reports. This task presents several challenges. First, a complete report contains multiple heterogeneous forms of information, including findings and tags. Second, abnormal regions in medical images are difficult to identify. Third, the re- ports are typically long, containing multiple sentences. To cope with these challenges, we (1) build a multi-task learning framework which jointly performs the pre- diction of tags and the generation of para- graphs, (2) propose a co-attention mechanism to localize regions containing abnormalities and generate narrations for them, (3) develop a hierarchical LSTM model to generate long paragraphs. We demonstrate the effectiveness of the proposed methods on two publicly available datasets.