Magnetic fields play an important role in astrophysics. This can have consequences for us on earth. Imagine yourself in an airbus that relies on the Global Positioning System (GPS). Suddenly, GPS doesn't work either because the signal fades (irregularities in the ionosphere produce diffraction and refraction effects) or because the satellites have to be shut off for some 15 min if there is a severe magnetic storm between us and the sun. Most of the time one can do without GPS, but if you hit some air turbulence and the plane drops by 500 meters, you better be careful not to hit another plane on your new course! This is just one reason to be concerned with the magnetic activity of the sun. Its activity varies cyclicly with a period of 7-17 years, and it does contribute to the change of the Earth's global climate, so its not all because of the greenhouse effect! The little ice age in the 17th century was clearly caused by the so-called Maunder minimum - a time when the sun was almost completely inactive and didn't exhibit any spots. A group at NORDITA is currently working on understanding the mechanism responsible for generating magnetic fields in the sun and also other stars where long-term cyclic variations have been detected. This is done using large scale numerical simulations on computers in Denmark, Norway, and the UK. An important theoretical finding has been the generation of large-scale magnetic fields by helical isotropic turbulence, which led to a new understanding of the nonlinear effects causing the saturation of a self-excited homogeneous dynamo. Magnetic helicity has emerged as a valuable theoretical tool, which predicts that the generation of twisted magnetic fields is accomanied by the generation of oppositely twisted magnetic fields. Easy reading: Brandenburg, A.: 2001, ``Magnetic mysteries,'' Science 292, 2440-2441 (http://www.sciencemag.org/cgi/content/summary/292/5526/2440) Review: Brandenburg, A., & Subramanian, K.: 2005, ``Astrophysical magnetic fields and nonlinear dynamo theory,'' Phys. Rep. 417, 1-209 (astro-ph/0405052, ADS, PDF) Other important papers: Brandenburg, A.: 2001, ``The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence,'' Astrophys. J. 550, 824-840 (astro-ph/0006186, ADS) Blackman, E. G. & Brandenburg, A.: 2002, ``Dynamic nonlinearity in large scale dynamos with shear,'' Astrophys. J. 579, 359-373 (astro-ph/0204497, ADS) Brandenburg, A.: 2005, ``The case for a distributed solar dynamo shaped by near-surface shear,'' Astrophys. J. 625, 539-547 (astro-ph/0502275, ADS, PDF) Brandenburg, A., Rädler, K.-H., Rheinhardt, M., & Käpylä, P. J.: 2008, ``Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence,'' Astrophys. J. 676, 740-751 (arXiv:0710.4059, ADS, PDF)