Deep neural networks (DNNs) have demonstrated remarkable performance for various applications, meanwhile, they are widely known to be vulnerable to the attack of adversarial perturbations. This intriguing phenomenon 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. The advantage of UAP is that it can be generated beforehand and then be applied on-the-fly during the attack. 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. Additionally, universal attacks in a wide range of applications beyond deep classification are also covered.