Quasinormal modes (QNMs) are eigenmodes of dissipative systems, particularly relevant in gravitational physics. They arise from perturbations of black hole (BH) or black brane spacetimes and are characterized by complex frequencies, with the imaginary part representing the decay rate of the perturbation. QNMs are crucial for understanding the dynamics of BHs and their interactions with surrounding matter, as well as for testing general relativity and other theories of gravity. In astrophysics, QNMs can be detected via gravitational wave observations, allowing precise measurements of BH mass and spin. In the context of gauge-gravity duality, QNMs serve as poles of retarded correlators, providing insights into the transport properties of strongly coupled quantum field theories. This review provides an overview of QNMs in various spacetime geometries, including asymptotically flat, anti-de Sitter (AdS), and de Sitter (dS) spacetimes. It discusses the methods used to compute QNMs, such as the WKB approximation, monodromy technique, and continued fraction method. The review also covers the QNM spectra of different BH types, including Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman BHs, as well as their AdS counterparts. The role of QNMs in gravitational wave astronomy and their implications for testing the no-hair theorem are also discussed. The review highlights the importance of QNMs in understanding the behavior of BHs and their interactions with matter, as well as their applications in theoretical physics, particularly in the context of gauge-gravity duality. It also addresses recent developments in the field, including the study of QNMs in higher-dimensional spacetimes and their connections to black hole phase transitions and analogue black holes. The review concludes with an outlook on future research directions and the potential for further advancements in the study of QNMs.Quasinormal modes (QNMs) are eigenmodes of dissipative systems, particularly relevant in gravitational physics. They arise from perturbations of black hole (BH) or black brane spacetimes and are characterized by complex frequencies, with the imaginary part representing the decay rate of the perturbation. QNMs are crucial for understanding the dynamics of BHs and their interactions with surrounding matter, as well as for testing general relativity and other theories of gravity. In astrophysics, QNMs can be detected via gravitational wave observations, allowing precise measurements of BH mass and spin. In the context of gauge-gravity duality, QNMs serve as poles of retarded correlators, providing insights into the transport properties of strongly coupled quantum field theories. This review provides an overview of QNMs in various spacetime geometries, including asymptotically flat, anti-de Sitter (AdS), and de Sitter (dS) spacetimes. It discusses the methods used to compute QNMs, such as the WKB approximation, monodromy technique, and continued fraction method. The review also covers the QNM spectra of different BH types, including Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman BHs, as well as their AdS counterparts. The role of QNMs in gravitational wave astronomy and their implications for testing the no-hair theorem are also discussed. The review highlights the importance of QNMs in understanding the behavior of BHs and their interactions with matter, as well as their applications in theoretical physics, particularly in the context of gauge-gravity duality. It also addresses recent developments in the field, including the study of QNMs in higher-dimensional spacetimes and their connections to black hole phase transitions and analogue black holes. The review concludes with an outlook on future research directions and the potential for further advancements in the study of QNMs.