Computational fluid dynamics (CFD) is a branch of computational science that deals with solving the Navier - Stokes equation using numerical techniques. Traditional CFD codes use different numerical schemes to approximate different fluxes in the Navier - Stokes equation. This can result in inconsistencies in how the fluxes are calculated. The Gas Kinetic Scheme (GKS) utilizes the more general Boltzmann Equation to calculate the fluxes directly as moments of the particle distribution function. In the first part of the project Gas Kinetic Simulations are used to study Rayleigh-Taylor Instability (RTI). RTI characteristic is established in the continuum - rarefied transitional regime for different Mach and Reynolds numbers. At each Mach number, there exists a critical Reynolds number (Recr) below which flow is dominated by diffusive transport characteristic of rarefied flows. In the transitional regime (near Recr), significant bubble-spike asymmetry is observed. It is shown that the spike side is dominated by diffusive transport, whereas the bubble side is advective in nature. The metrics characterizing the advective and diffusive domains in this transitional regime are identified. In the second part of the project, RTI characteristics in fully rarefied regime are studied using Unified Gas Kinetic Schemes (UGKS). Instead of solving the conservation equation, UGKS solves the Boltzmann equation and is known to be valid across a wide range of Knudsen numbers. Using UGKS, simulations up to Kn ~ 0.1 are performed, and instability growth in this regime is studied. The results of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.