Climate change and increased urban population are two major concerns for society. Moving towards more sustainable energy solutions in the urban context by integrating renewable energy technologies supports decarbonizing the energy sector and climate change mitigation. A successful transition also needs adequate consideration of climate change including extreme events to ensure the reliable performance of energy systems in the long run. This review provides an overview of and insight into the progress achieved in the energy sector to adapt to climate change, focusing on the climate resilience of urban energy systems. The state-of-the-art methodology to assess impacts of climate change including extreme events and uncertainties on the design and performance of energy systems is described and discussed. Climate resilience is an emerging concept that is increasingly used to represent the durability and stable performance of energy systems against extreme climate events. However, it has not yet been adequately explored and widely used, as its definition has not been clearly articulated and assessment is mostly based on qualitative aspects. This study reveals that a major limitation in the state-of-the-art is the inadequacy of climate change adaptation approaches in designing and preparing urban energy systems to satisfactorily address plausible extreme climate events. Furthermore, the complexity of the climate and energy models and the mismatch between their temporal and spatial resolutions are the major limitations in linking these models. Therefore, few studies have focused on the design and operation of urban energy infrastructure in terms of climate resilience. Considering the occurrence of extreme climate events and increasing demand for implementing climate adaptation strategies, the study highlights the importance of improving energy system models to consider future climate variations including extreme events to identify climate resilient energy transition pathways.