The advent of massively parallel supercomputing has begun to permit explicit 3–D simulations of turbulent convection occurring within the cores of early-type main sequence stars. Such studies should complement the stellar structure and evolution efforts that have so far largely employed 1–D nonlocal mixing length descriptions for the transport, mixing and overshooting achieved by core convection. We have turned to A-type stars as representative of many of the dynamical challenges raised by core convection within rotating stars. The differential rotation and meridional circulations achieved deep within the star by the convection, the likelihood of sustained magnetic dynamo action there, and the bringing of fresh fuel into the core by overshooting motions, thereby influencing main sequence lifetimes, all constitute interesting dynamical questions that require detailed modelling of global-scale convection. Using our anelastic spherical harmonic (ASH) code tested on the solar differential rotation problem, we have conducted a series of 3–D spherical domain simulations that deal with a simplified description of the central regions of rotating A-type stars, i.e a convectively unstable core is surrounded by a stable radiative envelope. A sequence of 3–D simulations are used to assess the properties of the convection (its global patterns, differential rotation, meridional circulations, extent and latitudinal variation of the overshooting) as transitions are made between laminar and turbulent states by changing the effective diffusivities, rotation rates, and subadiabaticity of the radiative exterior. We report on the properties deduced from these models for both the extent of penetration and the profile of rotation sustained by the convection.