This comprehensive review paper aims to provide an in-depth analysis of the most recent developments in the applications of artificial intelligence (AI) techniques, with an emphasis on their critical role in the demand side of power distribution systems. This paper offers a meticulous examination of various AI models and a pragmatic guide to aid in selecting the suitable techniques for three areas: load forecasting, anomaly detection, and demand response in real-world applications. In the realm of load forecasting, the paper presents a thorough guide for choosing the most fitting machine learning and deep learning models, inclusive of reinforcement learning, in conjunction with the application of hybrid models and learning optimization strategies. This selection process is informed by the properties of load data and the specific scenarios that necessitate forecasting. Concerning anomaly detection, this paper provides an overview of the merits and limitations of disparate learning methods, fostering a discussion on the optimization strategies that can be harnessed to navigate the issue of imbalanced data, a prevalent concern in power system anomaly detection. As for demand response, we delve into the utilization of AI techniques, examining both incentive-based and price-based demand response schemes. We take into account various control targets, input sources, and applications that pertain to their use and effectiveness. In conclusion, this review paper is structured to offer useful insights into the selection and design of AI techniques focusing on the demand-side applications of future energy systems. It provides guidance and future directions for the development of sustainable energy systems, aiming to serve as a cornerstone for ongoing research within this swiftly evolving field.