An accurate description of turbulent core convection is necessary in order to build robust models of planetary core processes. Towards this end, we focus here on the physics of rapidly rotating convection. In particular, we present a closely coupled suite of advanced asymptotically-reduced theoretical models, efficient Cartesian direct numerical simulations (DNS) and laboratory experiments. Good convergence is demonstrated between these three approaches, showing that a comprehensive understanding of the dynamics appears to be within reach in our simplified rotating convection system. The goal of this paper is to review these findings, and to discuss their possible implications for planetary cores dynamics.