Recent years have seen an amazing development in our knowledge of the magnetic fields in the universe. The last ten years were crucial in our realization of the importance of the magnetic fields in galaxies. While a lot of the earlier data on our Galaxy depended on optical observations, the bulk of the recent results depend on radio measurements. The radio Zeeman effect gave us new information on magnetic fields in molecular clouds. The mapping of galaxies at several radio frequencies resulted in new knowledge about the large-scale magnetic fields in these basic building blocks of the universe. These exciting observations have led to new theoretical developments. In particular, the dynamo theory of flat objects received much attention since the observed large-scale structures can best be explained through the action of the dynamo effect. This review will attempt to summarise the observational evidence and to give viable explanations for the magnetic fields in galaxies.