The Sun and the giant planets rotate and possess deep shells of convection. Some basic aspects of prototypical global convection have been studied with a laboratory model operated in the microgravity environment of Spacelab 3 that flew on the space shuttle Challenger in May 1985. This experiment studied thermally driven circulations within a rotating hemispherical shell of fluid across which are imposed radial and latitudinal temperature gradients. The radial force of gravity is modelled by imposing a strong electric field across the shell, with dielectric polarization forces producing radial accelerations proportional to temperature. When the influence of rotation is large, the experiments yield north-south oriented columnar convection in equatorial and subequatorial regions. As the differential heating is increased, these roll-like cells interact with mid-latitude waves, ultimately being destroyed by turbulent, horizontally isotropic convection that moves down from the pole. When a significant equator-to-pole temperature difference is imposed on the boundaries, spiral waves develop on top of a strong meridional circulation. Intricate, non-axisymmetric, convective patterns that propagate in longitude and evolve in time are described. Schlieren visualizations of these laboratory flows are compared with three-dimensional nonlinear simulations.