This talk provides an overview of Rayleigh-Taylor instability, a fingering instability at the interface between two fluids of different densities, where the light fluid pushes the heavy fluid. The instability is characterized by the growth of irregularities at the interface, leading to the formation of spikes, bubbles, and turbulent mixing. The stability criterion is that the interface is stable when the heavy fluid pushes the light fluid, and unstable when the light fluid pushes the heavy fluid. The instability is influenced by factors such as surface tension, viscosity, compressibility, and density ratios. The talk discusses the phenomenology of Rayleigh-Taylor instability, including the growth of perturbations, the development of structures on spikes, and the interactions among bubbles. It also covers the linear and nonlinear modeling of the instability, with linear analysis showing that the growth rate of short wavelength perturbations is unbounded in the absence of surface tension. Nonlinear models, such as those by Fermi, Baker and Freeman, and Crowley and Levermore, provide insights into the behavior of spikes and bubbles. The talk also addresses the late stage of Rayleigh-Taylor instability, including bubble amalgamation, spike break-up, and turbulent mixing. It highlights the importance of three-dimensional calculations and the role of statistically distributed heterogeneities in the growth of the instability. The need for experiments to validate theoretical models is emphasized, as well as the potential for fractalized interfaces in chaotic limits. The talk concludes with a summary of critical issues, including the importance of three-dimensional calculations, the role of heterogeneities, and the potential for fractalized interfaces in chaotic limits.This talk provides an overview of Rayleigh-Taylor instability, a fingering instability at the interface between two fluids of different densities, where the light fluid pushes the heavy fluid. The instability is characterized by the growth of irregularities at the interface, leading to the formation of spikes, bubbles, and turbulent mixing. The stability criterion is that the interface is stable when the heavy fluid pushes the light fluid, and unstable when the light fluid pushes the heavy fluid. The instability is influenced by factors such as surface tension, viscosity, compressibility, and density ratios. The talk discusses the phenomenology of Rayleigh-Taylor instability, including the growth of perturbations, the development of structures on spikes, and the interactions among bubbles. It also covers the linear and nonlinear modeling of the instability, with linear analysis showing that the growth rate of short wavelength perturbations is unbounded in the absence of surface tension. Nonlinear models, such as those by Fermi, Baker and Freeman, and Crowley and Levermore, provide insights into the behavior of spikes and bubbles. The talk also addresses the late stage of Rayleigh-Taylor instability, including bubble amalgamation, spike break-up, and turbulent mixing. It highlights the importance of three-dimensional calculations and the role of statistically distributed heterogeneities in the growth of the instability. The need for experiments to validate theoretical models is emphasized, as well as the potential for fractalized interfaces in chaotic limits. The talk concludes with a summary of critical issues, including the importance of three-dimensional calculations, the role of heterogeneities, and the potential for fractalized interfaces in chaotic limits.