The development of automatic speaker verification （ASV） technology is profoundly affecting and changing the current human-computer interaction system. As the core speech function of some smart devices， ASV can accept the voice of the target speakers and accurately identify the speakers’ identities. In recent years， the rapid development of artificial intelligence technology has promoted the leapfrog development of ASV systems. However， with the development of artificial neural network and deep learning technology， more and more researchers begin to study the way to attack ASV systems. How to attack ASV systems through a series of processing of raw speech has been a hot topic in speech research in recent years. At present， the attack methods of ASV systems can be roughly divided into spoofing attacks and adversarial attacks. In this paper， the typical methods and basic principles of the two kinds of attacks are summarized， some problems existing in current attack methods are sorted out， the safety problems existing in the system of ASV are revealed， a brief outlook on the future development of ASV system security is given， and the development directions of improving the security and reliability of ASV systems are provided.