Over the past few years, significant progress has been made in the field of presentation attack detection (PAD) for automatic speaker recognition (ASV). This includes the development of new speech corpora, standard evaluation protocols and advancements in front-end feature extraction and back-end classifiers. The use of standard databases and evaluation protocols has enabled for the first time the meaningful benchmarking of different PAD solutions. This chapter summarises the progress, with a focus on studies completed in the last 3 years. The article presents a summary of findings and lessons learned from two ASVspoof challenges, the first community-led benchmarking efforts. These show that ASV PAD remains an unsolved problem and that further attention is required to develop generalised PAD solutions which have potential to detect diverse and previously unseen spoofing attacks.