Recent years have seen an amazing development in our knowledge of the
magnetic fields in the universe. The last ten years were crucial in ou
r realization Of the importance of the magnetic fields in galaxies. Wh
ile a lot of the earlier data on our Galaxy depended on optical observ
ations, the bulk of the recent results depend on radio measurements. T
he radio Zeeman effect gave us new information on magnetic fields in m
olecular clouds. The mapping of galaxies at several radio frequencies
resulted in new knowledge about the large-scale magnetic fields in the
se basic building blocks of the universe. These exciting observations
have led to new theoretical developments. In particular, the dynamo th
eory of flat objects received much attention since the observed large-
scale structures can best be explained through the action of the dynam
o effect. This review will attempt to summarise the observational evid
ence and to give viable explanations for the magnetic fields in galaxi
es.