Interstellar magnetic fields

For three decades, magnetic fields have been known to permeate interstellar space. Each decade focussed attention on a different problem concerning the role of magnetic fields in star formation, and developed distinct techniques for the solution of the respective problem. A historical perspective of this period is given first. Then theoretical studies of the role of magnetic fields in star formation are reviewed critically, with emphasis on the dynamical processes occuring in collapsing interstellar clouds and on the interplay between theory and observation. A synthesis in the form of a scenario, albeit incomplete, for star formation in magnetic clouds is given. Prospects for the solution, during the 1980's, for remaining fundamental problems are discussed, and the need for certain kinds of observations is emphasized.