The most serious risk to network security can arise from a zero-day attack. Zero-day attacks are challenging to identify as they exhibit unseen behavior. Intrusion detection systems (IDS) have gained considerable attention as an effective tool for detecting such attacks. IDS are deployed in network systems to monitor the network and to detect any potential threats. Recently, a lot of Machine learning (ML) and Deep Learning (DL) techniques have been employed in Intrusion Detection Systems, and it has been found that these techniques can detect zero-day attacks efficiently. This paper provides an overview of the background, importance, and different types of ML and DL techniques adopted for detecting zero-day attacks. Then it conducts a comprehensive review of recent ML and DL techniques for detecting zero-day attacks and discusses the associated issues. Further, we analyze the results and highlight the research challenges and future scope for improving the ML and DL approaches for zero-day attack detection.