Heating, Ventilation, and Air Conditioning (HVAC) systems account for 60-70% of residential electricity consumption in Oman, where extreme desert climates with temperatures regularly exceeding 45°C create substantial cooling demands. As climate change intensifies cooling requirements, optimizing HVAC control strategies has be-come critical for energy sustainability while maintaining occupant thermal comfort. This review systematically analyzes four smart HVAC control paradigms applicable to Omani residential buildings: Model Predictive Control, Deep Reinforcement Learning, Fuzzy Logic Control, and Internet of Things-based integrated approaches. We examine performance data from Oman and Gulf Cooperation Council case studies, including the GUtech EcoHaus net-zero energy building and large-scale retrofit program analyses, contextualized within Oman's policy framework. Our analysis reveals that Model Predictive Control strategies achieve energy savings of 16-40% while maintaining thermal comfort within acceptable Predicted Mean Vote ranges. Deep Reinforcement Learning-based controllers demonstrate superior adaptability to dynamic occupancy patterns with reported energy reductions of 17-23%. Case studies demonstrate realized energy savings ranging from 25-75% depending on intervention comprehensiveness and baseline building performance. These findings indicate that advanced control strategies offer significant potential for reducing residential energy consumption in extreme heat climates when integrated with high-performance building envelopes. Future work should prioritize the development of occupant-centric adaptive comfort models calibrated for extreme heat conditions, integration of distributed energy re-sources with HVAC systems, and context-specific control strategies that account for regional occupancy patterns and cultural preferences.