Abstract Evidence is presented that shows that magnetic fields pervade the entire interstellar medium including interstellar gas clouds of both low and high density. The magnetic field in the ‘seed’ gas from which the denser clouds form is 0.2-0.3 nT (1T — 104G). Zeeman effect measurements of neutral hydrogen show that stronger fields occur in denser clouds. These data, taken with the microtesla fields found in OH maser sources, indicate that magnetic flux is conserved during gravitational collapse of interstellar clouds from densities of ca. 5 to ca. 107 cm-3. Magnetic fields appear to play a major role in the formation of dense interstellar clouds. Furthermore there is a strong indication that the magnetic field direction is preserved during cloud collapse.