This dissertation explores bootstrap methods in theoretical and applied statistics, focusing on their computational challenges and practical applications. The author outlines the fundamental concepts of bootstrap methods, discusses the mathematical challenges behind them, and presents new theoretical results and practical applications. The work includes proofs of key theorems and discusses the limitations of traditional bootstrap methods, such as the i.i.d. bootstrap, and introduces generalized block bootstrap and weighted bootstrap techniques. The dissertation also covers topics from probability theory, time series analysis, extreme value theory, and copulas, which are essential for understanding and applying bootstrap methods. The author applies these methods to real-world data, including wind speed, precipitation, and temperature data, to model climate change and assess the reliability of statistical models. The work includes detailed theoretical results, practical applications, and a discussion of the limitations and challenges of bootstrap methods in various contexts. The author also acknowledges the support of their supervisor and colleagues, and highlights the importance of computational tools and statistical programming in the research. The dissertation provides a comprehensive overview of bootstrap methods, their theoretical foundations, and their practical applications in various fields of statistics and data analysis.This dissertation explores bootstrap methods in theoretical and applied statistics, focusing on their computational challenges and practical applications. The author outlines the fundamental concepts of bootstrap methods, discusses the mathematical challenges behind them, and presents new theoretical results and practical applications. The work includes proofs of key theorems and discusses the limitations of traditional bootstrap methods, such as the i.i.d. bootstrap, and introduces generalized block bootstrap and weighted bootstrap techniques. The dissertation also covers topics from probability theory, time series analysis, extreme value theory, and copulas, which are essential for understanding and applying bootstrap methods. The author applies these methods to real-world data, including wind speed, precipitation, and temperature data, to model climate change and assess the reliability of statistical models. The work includes detailed theoretical results, practical applications, and a discussion of the limitations and challenges of bootstrap methods in various contexts. The author also acknowledges the support of their supervisor and colleagues, and highlights the importance of computational tools and statistical programming in the research. The dissertation provides a comprehensive overview of bootstrap methods, their theoretical foundations, and their practical applications in various fields of statistics and data analysis.