<p>To maintain the effectiveness, dependability, and security of modern energy systems, analyzing and detecting anomalies in energy usage, such as electricity theft and unusual power consumption, is crucial as Smart Grid (SG) technologies become increasingly common. This survey paper comprehensively reviews the literature on energy consumption analysis and detection, focusing on detecting electricity theft and anomalous power consumption. The works that are considered in this paper are classified based on Machine Learning (ML), Deep Learning (DL), and hybrid models, to identify electricity theft and unusual power usage. Privacy preservation-based methodologies in the context of energy consumption research and summarize the survey articles. Furthermore, datasets used in electricity theft and anomalous power consumption detection, applications, challenges, and limitations related to detecting abnormal power usage and electricity theft are also discussed, and suggested future research paths to push the boundaries of this field of work. This survey study offers a thorough overview of current research trends and directions in energy consumption analysis and detection by synthesizing ideas from various studies. It benefits researchers, practitioners, and policymakers in the energy sector.</p>