The article by Louis M. Pecora and Thomas L. Carroll reviews the history and early work on synchronization in chaotic systems. Initially, they discovered that two chaotic systems, despite their positive Lyapunov exponents, could synchronize when coupled appropriately. This counterintuitive phenomenon was later formalized using conditional Lyapunov exponents, which depend on the coupling parameters. The authors describe their initial experiments with chaotic systems, including the Lorenz and Rössler systems, and the development of a physical circuit to demonstrate synchronization. They also discuss the discovery of synchronization in networks of oscillators, where the synchronization manifold is a flat hyperspace defined by the condition \(x_i = x_j\) for all oscillators. The article highlights the importance of the diagonalization of the coupling matrix to analyze the stability of the synchronized state. Additionally, it covers the concept of generalized synchronization, where the response system is not identical to the drive system but still exhibits synchronization. The authors also address the challenges of noise robustness in chaotic synchronization and the development of the Master Stability Function (MSF) for analyzing synchronization in arbitrary networks. Finally, they discuss future directions, including parameter estimation and the broader topic of collective behavior in networked systems.The article by Louis M. Pecora and Thomas L. Carroll reviews the history and early work on synchronization in chaotic systems. Initially, they discovered that two chaotic systems, despite their positive Lyapunov exponents, could synchronize when coupled appropriately. This counterintuitive phenomenon was later formalized using conditional Lyapunov exponents, which depend on the coupling parameters. The authors describe their initial experiments with chaotic systems, including the Lorenz and Rössler systems, and the development of a physical circuit to demonstrate synchronization. They also discuss the discovery of synchronization in networks of oscillators, where the synchronization manifold is a flat hyperspace defined by the condition \(x_i = x_j\) for all oscillators. The article highlights the importance of the diagonalization of the coupling matrix to analyze the stability of the synchronized state. Additionally, it covers the concept of generalized synchronization, where the response system is not identical to the drive system but still exhibits synchronization. The authors also address the challenges of noise robustness in chaotic synchronization and the development of the Master Stability Function (MSF) for analyzing synchronization in arbitrary networks. Finally, they discuss future directions, including parameter estimation and the broader topic of collective behavior in networked systems.