This review provides a comprehensive overview of Bell nonlocality, a fundamental concept in quantum information science. Bell's theorem, proven in 1964, states that the predictions of quantum theory cannot be explained by any local theory, leading to the discovery of nonlocal correlations. The review covers the main concepts and tools developed to describe and study these nonlocal correlations, including mathematical characterizations, Bell inequalities, and their applications in quantum information processing. Key topics include: 1. **Mathematical Characterization**: Definitions of nonlocal correlations, no-signaling, local, and quantum correlations. 2. **Bell Inequalities**: Derivation and properties of Bell inequalities, including the CHSH inequality, and their maximal quantum violations. 3. **Nonlocality in Quantum Theory**: Relations between nonlocality and quantum resources like entanglement and Hilbert space dimension. 4. **Applications**: Use of quantum nonlocality in communication complexity, quantum cryptography, and device-independent quantum information processing. 5. **Information-Theoretic Perspective**: Nonlocal correlations as a fundamental resource and their recovery from information-theoretic principles. 6. **Multipartite Nonlocality**: Concepts of genuine multipartite nonlocality and monogamy of correlations. 7. **Experimental Aspects**: Overview of experimental tests of Bell nonlocality, including violations of Bell inequalities and loopholes. The review emphasizes the technical aspects of Bell nonlocality, focusing on recent developments and practical applications, while also providing historical context and foundational discussions.This review provides a comprehensive overview of Bell nonlocality, a fundamental concept in quantum information science. Bell's theorem, proven in 1964, states that the predictions of quantum theory cannot be explained by any local theory, leading to the discovery of nonlocal correlations. The review covers the main concepts and tools developed to describe and study these nonlocal correlations, including mathematical characterizations, Bell inequalities, and their applications in quantum information processing. Key topics include: 1. **Mathematical Characterization**: Definitions of nonlocal correlations, no-signaling, local, and quantum correlations. 2. **Bell Inequalities**: Derivation and properties of Bell inequalities, including the CHSH inequality, and their maximal quantum violations. 3. **Nonlocality in Quantum Theory**: Relations between nonlocality and quantum resources like entanglement and Hilbert space dimension. 4. **Applications**: Use of quantum nonlocality in communication complexity, quantum cryptography, and device-independent quantum information processing. 5. **Information-Theoretic Perspective**: Nonlocal correlations as a fundamental resource and their recovery from information-theoretic principles. 6. **Multipartite Nonlocality**: Concepts of genuine multipartite nonlocality and monogamy of correlations. 7. **Experimental Aspects**: Overview of experimental tests of Bell nonlocality, including violations of Bell inequalities and loopholes. The review emphasizes the technical aspects of Bell nonlocality, focusing on recent developments and practical applications, while also providing historical context and foundational discussions.