Convection in a rotating layer of fluid has been the subject of a great deal of theoretical and experimental research. This problem is relevant to convectively driven fluid flows in the Earth’s atmosphere, ocean and interior and also in the Sun and other stars, where the influence of rotation is generally important. In general numerical simulations of rotationally constrained flows are unable to reach realistic parameter values, e.g., Reynolds (Re) and Richardson (Ri) numbers. In particular, low values of Rossby number (Ro), defining the extent of rotational constraint, compound the already prohibitive temporal and spatial restrictions present for high- Re simulations by engendering high frequency inertial waves and the development of thin (Ekman) boundary layers. Extensive explorations of low Rossby number - high Rayleigh number convection present a fundamental challenge for both laboratory experiments and DNS. While simulations of asymptotically reduced system of equations valid in the limit of strong rotation has provided some progress in characterizing the possible fluid states some important discrepancies still remain. In this talk Rapidly rotating Rayleigh-Bénard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments and asymptotic modeling.