In the face of climate change impacts, various concepts and theories have emerged to enhance the resilience of systems and businesses most affected by these changes. Quantifying the resilience of urban-built environments and communities has become crucial, and this chapter explores different methods and approaches for such assessments. It provides a comprehensive overview of the foundations of resilience recognition, examining the performance of urban systems as a key factor. The chapter delves into the methods and approaches used to estimate the resilience of urban environments, emphasizing the ability to compare different urban systems based on their resilience characteristics. Specifically, it focuses on diverse resilience frameworks and assessment approaches, including matrices, indices, and indicators employed for physical infrastructure. Real-world examples of existing frameworks and applications for various systems and networks are presented, offering insights into the practical implementation of resilience assessments. By highlighting the quantitative and qualitative dimensions of urban resilience assessment, this chapter equips researchers and practitioners with a broader understanding of the tools and techniques available to evaluate the resilience of urban systems, ultimately supporting the development of more resilient and adaptive cities.