  The current understanding of astrophysical magnetic fields is reviewed,
focusing on their generation and maintenance by turbulence. In the
astrophysical context this generation is usually explained by a self-excited
dynamo, which involves flows that can amplify a weak 'seed' magnetic field
exponentially fast. Particular emphasis is placed on the nonlinear saturation
of the dynamo. Analytic and numerical results are discussed both for small
scale dynamos, which are completely isotropic, and for large scale dynamos,
where some form of parity breaking is crucial. Central to the discussion of
large scale dynamos is the so-called alpha effect which explains the generation
of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has
kinetic helicity. Large scale dynamos produce small scale helical fields as a
waste product that quench the large scale dynamo and hence the alpha effect.
With this in mind, the microscopic theory of the alpha effect is revisited in
full detail and recent results for the loss of helical magnetic fields are
reviewed.
