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The complexity of an interconnected power system has grown exponentially with the increased load demands. These demands and stress conditions are the potential nodes in coupled system to challenge the control and stability of a multi-operational power system. Once these potential nodes are exploited, this could lead to developing stringent conditions and generation of power system oscillations which are required by the grid codes to be damped and controlled adequately. A poorly damped set of power oscillations may lead to system-wide breakups or considerably reduce the power transfer over critical channels and corridors. In recent years, a compelling need has arisen to understand the oscillation damping in the conventional and modern power grids for better performance management, control, and stability in power transfer. In this paper, a bibliographic review on the damping of power system oscillations is provided. The study identifies various control design techniques, technologies, and characteristics used in power systems. Moreover, it discusses various devices and tools to minimize damping during the era of conventional grids and renewable energy integration. The methodology of different approaches and their likely combination are discussed for different types of control design. This study also represents useful information for readers on the complete life-cycle and development phase of technology to minimize the instability variations in generating units, transmission lines, transformers, loads, and HVDC lines. A comprehensive list of publications to date in the open literature is compiled to portray a complete visual of different developments in this area. • Unstable power oscillations result in blackouts and reduced interarea power transfers. • Compel the need to understand oscillation dynamics and damping control in renewable rich grids. • Overview of analysis and control techniques, infrastructure and systems characteristics hitherto. • Classification of past and emerging oscillation frameworks from the perspective of smart grids. • Highlighting technology life cycle and development/deployment phases to minimize instability risk. • Comprehensive list of publications for a visual scenery of hitherto developments in this field. [ABSTRACT FROM AUTHOR]