Speech spoofing refers to the technology of counterfeiting an illegal speech without the authentication by automatic speaker verification （ASV） system to the speech of a legally authenticated speaker by ASV through recording， text-to-speech， voice conversion and other means， so as to achieve the goal of passing the ASV system. With the development of artificial intelligence and speech anti-spoofing methods， ASV systems have encountered severe challenges in security. It is a hot topic in the field of speech research in recent years to detect the authenticity of the speech input to the ASV system and to prevent spoof speech from passing the verification of ASV to improve the security of the ASV system. The latest research of scholars at home and abroad explores the influence of different speech spoofing methods on ASV system from the perspective of acoustic feature and recognition model， and further studies the corresponding speech anti-spoofing technology， which improves the anti-spoofing ability of ASV systems to a certain extent. This paper summarizes the latest methods of speech spoofing to ASV systems and the latest anti-spoofing methods， focusing on the state-of-the-art research results around the world， and prospects the development direction of speech anti-spoofing technology.