One of the most fascinating and challenging topics in physics and astrophysics is the understanding of the generation and
self-sustaining of magnetic fields in planets, stars, galaxies, etc. The most accredited mechanism is the so-called dynamo effect, i.e. the maintaining of a magnetic field against diffusive effects by the motion of electrically conducting fluids. Some of the examples of dynamo effect closest of our experience are the presence of the Earth and Sun magnetic field. Paleomagnetic measurements showed that the Earth's magnetic dipole reverses stochastically in time, with intervals ranging from 10^4 up to 10^7 years. On the other hand, Sun's magnetic field displays more regular polarity inversions mainly on a period of about 11 years, although recent observations indicate the presence of other periodicities. Many researchers have dealt with this problem using direct numerical simulations, and reduced models (mean field models, shell models, large eddy simulations): some of these models, are able to reproduce the observed features of the Earth and Sun dynamos, under the assumption of appropriate values of some critical parameters (alpha effect, differential rotation, etc.). The aim of this session is to review the state of the art on this topic, both under theoretical and numerical standpoints, and comparing with recent observations.