Anomaly detection is an important job in many different fields, such as cybersecurity, healthcare, finance, and industrial systems. In these areas, identifying deviations from typical behaviour may help avert large undesirable effects. Another important domain is industrial systems. When confronted with the complexity and high dimensionality of current datasets, traditional approaches for anomaly identification sometimes fail to identify anomalies. In order to solve these issues, machine learning methodologies, and more specifically deep learning techniques, have emerged as formidable tools. The purpose of this work is to present a complete review of machine learning algorithms for anomaly identification. These techniques include supervised, unsupervised, and semi-supervised methods. We investigate the recent developments in deep learning models, including Autoencoders, Generative Adversarial Networks (GANs), and Recurrent Neural Networks (RNNs), as well as the applications of these models in anomaly detection. In order to successfully evaluate the performance of these models, evaluation criteria and procedures are given. In addition to this, we investigate a wide range of real-world applications and case studies, focussing on the effect that machine learning-based anomaly detection has had in a variety of industries.