The intriguing phenomenon of adversarial examples has attracted significant attention in machine learning and what might be more surprising to the community is the existence of universal adversarial perturbations (UAPs), i.e. a single perturbation to fool the target DNN for most images. With the focus on UAP against deep classifiers, this survey summarizes the recent progress on universal adversarial attacks, discussing the challenges from both the attack and defense sides, as well as the reason for the existence of UAP. We aim to extend this work as a dynamic survey that will regularly update its content to follow new works regarding UAP or universal attack in a wide range of domains, such as image, audio, video, text, etc. Relevant updates will be discussed at: https://bit.ly/2SbQlLG. We welcome authors of future works in this field to contact us for including your new findings.