The problem of convection in rotating spherical fluid shells is reviewed with emphasis on recently obtained results. The generation of magnetic fields by convection shows a strong dependence on the Prandtl number P of the fluid. Results for the computationally accessible regime of convection driven dynamos in the parameter space are given and the validity of the magnetostrophic approximation is discussed. Of particular interest are various types of dipole oscillations, reversals and torsional oscillations.