The urban energy infrastructure is facing a rising number of challenges due to climate change and rapid urbanization. In particular, the link between urban morphology and energy systems has become increasingly crucial as cities continue to expand and become more densely populated. Achieving climate neutrality adds another layer of complexity, highlighting the need to address this relationship to develop effective strategies for sustainable urban energy infrastructure. The occurrence of extreme climate events can also trigger cascading failures in the system components, leading to long-lasting blackouts. This review paper thoroughly explores the challenges of incorporating urban morphology into energy system models through a comprehensive literature review and proposes a new framework to enhance the resilience of interconnected systems. The review emphasizes the need for integrated models to provide deeper insights into urban energy systems design and operation and addresses the cascading failures, interconnectivity, and compound impacts of climate change and urbanization on energy systems. It also explores emerging challenges and opportunities, including the requirement for high-quality data, utilization of big data, and integration of advanced technologies like artificial intelligence and machine learning in urban energy systems. The proposed framework integrates urban morphology classification, mesoscale and microscale climate data, and a design and operation process to consider the influence of urban morphology, climate variability, and extreme events. Given the prevalence of extreme climate events and the need for climate-resilient strategies, the study underscores the significance of improving energy system models to accommodate future climate variations while recognizing the interconnectivity within urban infrastructure.