Claimed identities of speakers can be verified by means of automatic speaker verification (ASV) systems, also known as voice biometric systems. Focusing on security and robustness against spoofing attacks on ASV systems, and observing that the investigation of attacker’s perspectives is capable of leading the way to prevent known and unknown threats to ASV systems, several countermeasures (CMs) have been proposed during ASVspoof 2015, 2017, 2019, and 2021 challenge campaigns that were organized during INTERSPEECH conferences. Furthermore, there is a recent initiative to organize the ASVSpoof 5 challenge with the objective of collecting the massive spoofing/deepfake attack data (i.e., phase 1), and the design of a spoofing-aware ASV system using a single classifier for both ASV and CM, to design integrated CM-ASV solutions (phase 2). To that effect, this paper presents a survey on a diversity of possible strategies and vulnerabilities explored to successfully attack an ASV system, such as target selection, unavailability of global countermeasures to reduce the attacker’s chance to explore the weaknesses, state-of-the-art adversarial attacks based on machine learning, and deepfake generation. This paper also covers the possibility of attacks, such as hardware attacks on ASV systems. Finally, we also discuss the several technological challenges from the attacker’s perspective, which can be exploited to come up with better defence mechanisms for the security of ASV systems.