Invalid signatures produced by some adversaries may pose a severe challenge to the recipient. Furthermore, identifying an invalid signature in a bunch of messages could be a complex and challenging task to do. Batch verification is an idea to simultaneously verify multiple digital signatures in just one exponential operation time. By this scheme, we can make a quick response, and improve the verification time. In terms of identifying illegal signatures in the batch of messages, we have surveyed several well-known papers that proposed different approaches. In this paper, we define four criteria for evaluating these schemes. It is followed by a detailing review and computation comparisons from all documents. Finally, we provide two issues for future works.