In what is famously known as the solar activity cycle, every 11 years a wave of quasistationary magnetic field propagates in the solar convective zone from the middle latitudes equatorwards, driven by the dynamo jointly produced by the differential rotation and mirrorasymmetric convection. Similar processes occur in other celestial bodies and can to some extent be reproduced in the lab environment. This paper reviews the current status of and future trends in the study of the dynamo problem.