The rapid advancements in power systems have facilitated the introduction of smart grids (SGs), which enable bidirectional communication between utilities and consumers. A critical component of SGs is the Home Energy Management System (HEMS), which plays a significant role in Demand-Side Management (DSM) to ensure grid stability. Traditional optimization techniques used in HEMS are being increasingly complemented and replaced by Artificial Intelligence (AI)-based methods due to their superior performance. This review paper explores various AI-driven optimization techniques, like Deep Learning (DL) and Machine Learning (ML) algorithms, and their applications in HEMS. It discusses the architecture of HEMS, including smart controllers, smart meters, Renewable Energy Sources (RES), Energy Storage Systems (ESS), and Electric Vehicles (EVs), and highlights the importance of communication technologies in these systems. The paper also examines different DSM programs and optimization strategies for scheduling appliances, providing a detailed literature survey on meta-heuristic, ML, and DL approaches. The findings indicate that AI-based techniques significantly enhance energy efficiency and user comfort, marking a shift towards more intelligent and sustainable energy management solutions. This review aims to give a clear overview of the current situation and future possibilities of AI in HEMS.