Radio synchrotron emission is a powerful tool to study the strength and structure of magnetic fields in galaxies. Unpolarized synchrotron emission traces isotropic turbulent fields which are strongest in spiral arms and bars (20-30 mu G) and in central starburst regions (50-100 mu G). Such fields are dynamically important; they affect gas flows and drive gas inflows in central regions. -- Polarized emission traces ordered fields, which can be regular or anisotropic turbulent, where the latter originates from isotropic turbulent fields by the action of compression or shear. The strongest ordered fields (10-15 mu G) are generally found in interarm regions. In galaxies with strong density waves, ordered fields are also observed at the inner edges of spiral arms. Ordered fields with spiral patterns exist in grand-design, barred and flocculent galaxies, and in central regions. Ordered fields in interacting galaxies have asymmetric distributions and are a tracer of past interactions between galaxies or with the intergalactic medium. In radio halos around edge-on galaxies, ordered magnetic fields with X-shaped patterns are observed. -- Faraday rotation measures of the diffuse polarized radio emission from galaxy disks reveal large-scale spiral patterns that can be described by the superposition of azimuthal modes; these are signatures of regular fields generated by mean-field dynamos. Magnetic arms between gaseous spiral arms may also be products of dynamo action, but need a stable spiral pattern to develop. Helically twisted field loops winding around spiral arms were found in two galaxies so far. Large-scale field reversals, like the one found in the Milky Way, could not yet be detected in external galaxies. -- The origin and evolution of cosmic magnetic fields will be studied with forthcoming radio telescopes like the Square Kilometre Array.
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