The article reviews the development and application of the Quantum Jump approach to dissipative dynamics in quantum optics. It begins by discussing the challenges of describing single quantum systems due to the coupling to a large reservoir, leading to irreversible energy loss. Traditional methods, such as density matrices and Master equations, are insufficient for this purpose. The Quantum Jump approach, which focuses on individual realizations conditioned on specific observation records, has emerged as a powerful tool. This approach is applied to various problems in quantum optics, including intermittent fluorescence, ensemble behavior, and the dynamics of single quantum systems. The article also explores the theoretical foundations of the Quantum Jump approach, including its derivation and connection to other methods like Monte Carlo Wavefunction and Quantum Trajectory methods. It highlights the practical applications of these methods, such as in laser cooling and quantum computing, and discusses their advantages over traditional ensemble descriptions. The review concludes with a discussion of the Quantum Jump approach's potential for simulating complex problems and its role in advancing our understanding of dissipative processes in quantum systems.The article reviews the development and application of the Quantum Jump approach to dissipative dynamics in quantum optics. It begins by discussing the challenges of describing single quantum systems due to the coupling to a large reservoir, leading to irreversible energy loss. Traditional methods, such as density matrices and Master equations, are insufficient for this purpose. The Quantum Jump approach, which focuses on individual realizations conditioned on specific observation records, has emerged as a powerful tool. This approach is applied to various problems in quantum optics, including intermittent fluorescence, ensemble behavior, and the dynamics of single quantum systems. The article also explores the theoretical foundations of the Quantum Jump approach, including its derivation and connection to other methods like Monte Carlo Wavefunction and Quantum Trajectory methods. It highlights the practical applications of these methods, such as in laser cooling and quantum computing, and discusses their advantages over traditional ensemble descriptions. The review concludes with a discussion of the Quantum Jump approach's potential for simulating complex problems and its role in advancing our understanding of dissipative processes in quantum systems.