The availability of smart devices leads to an exponential increase in multimedia content. However, the rapid advancements in deep learning have given rise to sophisticated algorithms capable of manipulating or creating multimedia fake content, known as Deepfake. Audio Deepfakes pose a significant threat by producing highly realistic voices, thus facilitating the spread of misinformation. To address this issue, numerous audio anti-spoofing detection challenges have been organized to foster the development of anti-spoofing countermeasures. This survey paper presents a comprehensive review of every component within the detection pipeline, including algorithm architectures, optimization techniques, application generalizability, evaluation metrics, performance comparisons, available datasets, and open-source availability. For each aspect, we conduct a systematic evaluation of the recent advancements, along with discussions on existing challenges. Additionally, we also explore emerging research topics on audio anti-spoofing, including partial spoofing detection, cross-dataset evaluation, and adversarial attack defence, while proposing some promising research directions for future work. This survey paper not only identifies the current state-of-the-art to establish strong baselines for future experiments but also guides future researchers on a clear path for understanding and enhancing the audio anti-spoofing detection mechanisms.