Blind image super-resolution (SR), aiming to super-resolve low-resolution images with unknown degradation, has attracted increasing attention due to its significance in promoting real-world applications. Many novel and effective solutions have been proposed recently, especially with powerful deep learning techniques. Despite years of efforts, it still remains as a challenging research problem. This paper serves as a systematic review on recent progress in blind image SR, and proposes a taxonomy to categorize existing methods into three different classes according to their ways of degradation modelling and the data used to solve the SR model. This taxonomy helps summarize and distinguish among existing methods. We hope to provide insights into current research states, as well as revealing novel research directions worth exploring. In addition, we make a summary on commonly used datasets and previous competitions related to blind image SR. Last but not least, a comparison among different methods is provided with detailed analysis on their merits and demerits using both synthetic and real testing images.