A global surge in climate-energy policies signifies the shared recognition of the urgent imperative to combat climate change and transition to renewable and sustainable energy systems. These goals mark a significant shift toward a decarbonized future, exemplifying governments' commitment at all levels to address the pressing challenges posed by climate change. However, the integration of renewable resources introduces a considerable degree of variability and uncertainty, which poses challenges for both day-to-day system operation and long-term grid planning. Regarding daily operations, the decentralized system demands attention to innovative control strategies that effectively harness intermittent renewable resources while maintaining reliability and economic expectations. This calls for effective utilization of renewable resources to meet emission reduction targets while ensuring grid reliability and economic efficiency. In terms of long-term planning, the dynamic nature of climatic and technological changes adds complexity, necessitating a delicate balance between supply and demand within the system as the penetration level of renewable energy increases. The challenges for the planning and control problems require distinct formulation for the problems on different time scales. Therefore, this dissertation is structured in two major directions by using advanced modeling and algorithmic tools to facilitate the clean energy transition: 1) to design adaptive robust decision-making frameworks for the short-term energy management of distributed power systems considering multiple potentially conflicting objectives; and 2) to develop practical models that capture the intricacies of the energy system and identify the vulnerability of the future carbon-free energy system under long-term climate and technology changes for system planning The main conclusions drawn from this research are: 1) The proposed robust adaptive decision-making framework demonstrates significant improvements in the energy management of the Cornell campus microgrid. Across all objectives considered, the framework outperforms the current operating strategy implemented on campus, showcasing its potential for enhancing the system's performance. 2) The vulnerability of the future power system exhibits spatio-temporal heterogeneity, driven by the seasonal and daily variability of renewable resources and transmission bottlenecks. This finding emphasizes the need to consider these factors in planning and decision-making processes. 3) The observed spatiotemporal heterogeneity highlights the importance of efficient utilization of renewable resources. Blindly expanding renewable energy capacity without considering the specific characteristics of different locations and seasons can result in suboptimal resource utilization. These findings contribute to the understanding of clean energy transitions and provide valuable information to policymakers, grid operators, and stakeholders. By leveraging advanced modeling techniques and decision-making frameworks, this research contributes to the advancement of sustainable and efficient energy systems.