Magnetic field is present in many astrophysical objects including stars, planets, galaxies etc. How magnetic field is generated in these objects is an unsolved puzzle in physics. First qualitative idea to explain this phenomena is due to Larmer (1919); he suggested that the currents in the plasma of the stars and planets generate magnetic field, which in turn enhances the magnetic field (bootstrap). Cowling, Elsasser, Parker, Batchelor have constructed interesting models to explain dynamo.
Another interesting theory of dynamo is called -dynamo due to Steenbeck (1966), and Krause and Radler in which the random helical velocity field generates magnetic field, but the back-reaction of the magnetic field on the velocity field is ignored. Later Pouquet et al., Kulsrud and Anderson, Chou, Brandenburg and others have considered the back-reaction, and discussed about the dynamic models of dynamo.
There was a breakthrough experiment by French group (Manchaux et al.) where they observed dynamo in a cylindrical setup containing turbulent liquid sodium. There are recent high-resolution simulations (Schekochihin et al., Ponty et al.) that investigate the mechanism of magnetic field growth in full MHD equations.