The strength of the total magnetic field in our Milky Way from radio Zeeman and synchrotron measurements is about 6 muG near the Sun and several mG in dense clouds, pulsar wind nebulae, and filaments near the Galactic Center. Diffuse polarized radio emission and Faraday rotation of the polarized emission from pulsars and background sources show many small-scale magnetic features, but the overall field structure in our Galaxy is still under debate. -- Radio synchrotron observations of nearby galaxies reveal dynamically important magnetic fields of 10-30 muG total strength in the spiral arms. Fields with random orientations are concentrated in spiral arms, while ordered fields (observed in radio polarization) are strongest in interarm regions and follow the orientation of the adjacent gas spiral arms. Faraday rotation of the diffuse polarized radio emission from the disks of spiral galaxies sometimes reveals large-scale patterns which are signatures of coherent fields generated by dynamos, but in most galaxies the field structure is more complicated. -- Strong magnetic fields are also observed in radio halos around edge-on galaxies, out to large distances from the plane. The synchrotron scaleheight of radio halos allows to measure the mean outflow velocity of the cosmic-ray electrons. The ordered halo fields mostly form an X-shaped pattern, but no large-scale pattern is seen in the Faraday rotation data. Diffuse polarized radio emission in the outer disks and halos is an excellent tracer of galaxy interactions and ram pressure by the intergalactic medium. -- Intracluster gas can also be significantly magnetized and highly polarized due to shocks or cluster mergers.
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