Audio has become an increasingly crucial biometric modality due to its ability to provide an intuitive way for humans to interact with machines. It is currently being used for a range of applications including person authentication to banking to virtual assistants. Research has shown that these systems are also susceptible to spoofing and attacks. Therefore, protecting audio processing systems against fraudulent activities such as identity theft, financial fraud, and spreading misinformation, is of paramount importance. This paper reviews the current state-of-the-art techniques for detecting audio spoofing and discusses the current challenges along with open research problems. The paper further highlights the importance of considering the ethical and privacy implications of audio spoofing detection systems. Lastly, the work aims to accentuate the need for building more robust and generalizable methods, the integration of automatic speaker verification and countermeasure systems, and better evaluation protocols.