The article reviews the quantum jump approach to dissipative dynamics in quantum optics, focusing on theoretical methods for describing individual quantum systems. It discusses how dissipation arises from coupling to a larger environment, leading to irreversible decay. Traditional methods used density matrices, but new approaches, such as quantum jump, Monte Carlo wavefunction, and quantum trajectory methods, allow for the description of single-system dynamics conditioned on observation records. These methods are applied to various problems in quantum optics, including intermittent fluorescence, photon statistics, and resonance fluorescence. The quantum jump approach provides a framework for understanding single-system dynamics, enabling the simulation of complex processes that were previously intractable with master equations. The article also highlights the importance of these methods in experimental studies of single quantum systems, such as trapped ions, and their applications in quantum computing and laser cooling. Theoretical developments, including the derivation of quantum jump equations and their relation to ensemble descriptions, are discussed, along with their implications for understanding quantum coherence and dissipation. The review emphasizes the utility of these methods in both theoretical and experimental contexts, offering insights into the behavior of quantum systems under various conditions.The article reviews the quantum jump approach to dissipative dynamics in quantum optics, focusing on theoretical methods for describing individual quantum systems. It discusses how dissipation arises from coupling to a larger environment, leading to irreversible decay. Traditional methods used density matrices, but new approaches, such as quantum jump, Monte Carlo wavefunction, and quantum trajectory methods, allow for the description of single-system dynamics conditioned on observation records. These methods are applied to various problems in quantum optics, including intermittent fluorescence, photon statistics, and resonance fluorescence. The quantum jump approach provides a framework for understanding single-system dynamics, enabling the simulation of complex processes that were previously intractable with master equations. The article also highlights the importance of these methods in experimental studies of single quantum systems, such as trapped ions, and their applications in quantum computing and laser cooling. Theoretical developments, including the derivation of quantum jump equations and their relation to ensemble descriptions, are discussed, along with their implications for understanding quantum coherence and dissipation. The review emphasizes the utility of these methods in both theoretical and experimental contexts, offering insights into the behavior of quantum systems under various conditions.