Automatically generating radiology reports can improve current clinical practice in diagnostic radiology. On one hand, it can relieve radiologists from the heavy burden of report writing; On the other hand, it can remind radiologists of abnormalities and avoid the misdiagnosis and missed diagnosis. Yet, this task remains a challenging job for data-driven neural networks, due to the serious visual and textual data biases. To this end, we propose a Posterior-and-Prior Knowledge Exploring-and-Distilling approach (PPKED) to imitate the working patterns of radiologists, who will first examine the abnormal regions and assign the disease topic tags to the abnormal regions, and then rely on the years of prior medical knowledge and prior working experience accumulations to write reports. Thus, the PPKED includes three modules: Posterior Knowledge Explorer (PoKE), Prior Knowledge Explorer (PrKE) and Multi-domain Knowledge Distiller (MKD). In detail, PoKE explores the posterior knowledge, which provides explicit abnormal visual regions to alleviate visual data bias; PrKE explores the prior knowledge from the prior medical knowledge graph (medical knowledge) and prior radiology reports (working experience) to alleviate textual data bias. The explored knowledge is distilled by the MKD to generate the final reports. Evaluated on MIMIC-CXR and IU-Xray datasets, our method is able to outperform previous state-of-the-art models on these two datasets. Lungs are clear. No pleural effusions or pneumothoraces. Heart and mediastinum of normal size and contour. 1 scoliosis. 1 There is a scoliosis. No acute cardiopulmonary abnormality. There is no pleural effusion. No evidence of pneumothorax. The lungs are clear. There is no focal airspace consolidation. Heart size is normal. There is a moderate right sided pneumothorax with tip in the right atrium. There is a moderate right sided pneumothorax with large pleural effusion. No pneumothorax masses. No pneumothorax masses. No acute bony abnormalities.