This review focuses on continuous-variable quantum information processes that rely on Gaussian states, operations, and channels. Gaussian states are continuous-variable states represented by Gaussian functions, and Gaussian operations transform these states into other Gaussian states. The review covers the theoretical and experimental aspects of Gaussian quantum information, including simple analytical tools and readily available optical components. It discusses a wide range of tasks and applications, such as quantum communication, cryptography, computation, teleportation, and state discrimination. The review also covers recent developments in the field, from basic theoretical tools to landmark experimental realizations. Key topics include the elements of Gaussian quantum information theory, examples of Gaussian states and operations, symplectic analysis for multimode Gaussian states, entanglement in bipartite Gaussian states, and measuring Gaussian states. The review further explores Gaussian quantum protocols, bosonic Gaussian channels, continuous-variable quantum cryptography, and quantum computation using Gaussian cluster states. Finally, it provides perspectives and concluding remarks on the future directions of research in Gaussian quantum information.This review focuses on continuous-variable quantum information processes that rely on Gaussian states, operations, and channels. Gaussian states are continuous-variable states represented by Gaussian functions, and Gaussian operations transform these states into other Gaussian states. The review covers the theoretical and experimental aspects of Gaussian quantum information, including simple analytical tools and readily available optical components. It discusses a wide range of tasks and applications, such as quantum communication, cryptography, computation, teleportation, and state discrimination. The review also covers recent developments in the field, from basic theoretical tools to landmark experimental realizations. Key topics include the elements of Gaussian quantum information theory, examples of Gaussian states and operations, symplectic analysis for multimode Gaussian states, entanglement in bipartite Gaussian states, and measuring Gaussian states. The review further explores Gaussian quantum protocols, bosonic Gaussian channels, continuous-variable quantum cryptography, and quantum computation using Gaussian cluster states. Finally, it provides perspectives and concluding remarks on the future directions of research in Gaussian quantum information.