Linearly polarized radio continuum emission is a powerful tool for studying the strength and structure of interstellar magnetic fields in galaxies. Interstellar magnetic fields with a well–ordered spiral structure exist in grand–design, flocculent and even irregular galaxies. In grand–design galaxies the fields are aligned parallel to the optical spiral arms, but the strongest regular fields are found in interarm regions, sometimes forming ‘magnetic spiral arms’ between the optical spiral arms. Processes related to star formation tangle the field in the spiral arms. Faraday rotation of the polarization vectors shows patterns which support the existence of coherent large–scale fields in galactic discs. In a few galaxies an axisymmetric spiral pattern dominates, while others host a bisymmetric spiral field or a superposition of dynamo modes. In the majority of axisymmetric cases the field is directed inwards. In barred galaxies the magnetic field seems to follow the gas flow within the bar. The location of the shock front in the magnetic field deviates from that expected from hydrodynamical models. Within (and interior to) the circumnuclear ring the field is again of spiral shape, which leads to magnetic stresses, possibly driving gas inflow towards the active nucleus. The next–generation radio telescopes should be able to reveal the wealth of magnetic structures in galaxies.