The advancement of communication and internet technology has brought risks to network security. Thus, Intrusion Detection Systems (IDS) was developed to combat malicious network attacks. However, IDSs still struggle with accuracy, false alarms, and detecting new intrusions. Therefore, organizations are using Machine Learning (ML) and Deep Learning (DL) algorithms in IDS for more accurate attack detection. This paper provides an overview of IDS, including its classes and methods, the detected attacks as well as the dataset, metrics, and performance indicators used. A thorough examination of recent publications on IDS-based solutions is conducted, evaluating their strengths and weaknesses, as well as a discussion of their potential implications, research challenges, and new trends. We believe that this comprehensive review paper covers the most recent advances and developments in ML and DL-based IDS, and also facilitates future research into the potential of emerging Artificial Intelligence (AI) to address the growing complexity of cybersecurity challenges.