Security of automatic speaker verification (ASV) systems is compromised by various spoofing attacks. While many types of non-proactive attacks (and their defenses) have been studied in the past, attacker's perspective on ASV, represents a far less explored direction. It can potentially help to identify the weakest parts of ASV systems and be used to develop attacker-aware systems. We present an overview on this emerging research area by focusing on potential threats of adversarial attacks on ASV, spoofing countermeasures, or both. We conclude the study with discussion on selected attacks and leveraging from such knowledge to improve defense mechanisms against adversarial attacks.