In inertial confinement fusion, a shell of solid thermonuclear fuel (deuterium and tritium) is imploded by irradiating its surface directly with UV laser light (direct drive) or indirectly with laser-produced x rays (indirect drive). In both cases, the dynamics of the implosion is governed by the laws of hydrodynamics. Conservation of mass and momentum are the same as the ones describing classical fluid mechanics. The conservation of energy is complicated by the energy transfer between the laser or x-ray radiation field and the plasma internal or kinetic energy. Classical fluid mechanics including radiation energy transport is usually referred to as “radiative hydrodynamics.” The latter is a well-known discipline in astrophysics. In ICF, radiative hydrodynamics is used to predict the implosion dynamics and the level of shell distortion induced by hydrodynamic instabilities. In astrophysics, radiative hydrodynamics is used to study the dynamics of stars. The main obstacle to reaching thermonuclear ignition is the onset of the so-called “Rayleigh-Taylor instability (RTI)” at the outer and inner surfaces of the imploding shell. The RTI occurs when a heavy fluid is accelerated against a light fluid. In ICF, the heavy fluid is the compressed target accelerated by the low-density ablating plasma (the light fluid). Because of its devastating effects on ICF implosions (a small perturbation could grow thousands of times during the implosion), it is important to fully understand the physics and the stabilizing mechanisms of such instability. Although the physics of the RTI for two inviscid superimposed fluids is well known, the RTI in laser-accelerated targets is strongly affected by the laser ablation, the electron and radiation energy transport, and the complicated density profiles. Two- and three-dimensional numerical simulations as well as complicated analytic theories have been developed at LLE to predict the evolution of the RTI. Such theories and simulations have been compared with detailed experimental observations. The experimental campaigns carried out using the OMEGA laser system have produced a set of reliable data allowing the validation of the hydrodynamic codes and theories developed at LLE. The RTI also plays an important role in the dynamics of astrophysical objects such as supernovae. Recent images from the Hubble Space Telescope of the supernova SN1987A remnant have indicated the development of the RTI in the supernova ejecta as denser ejecta are being accelerated by less-dense ejecta.