We discuss the effects of the magnetic field observed in molecular clouds on the process of star formation, concentrating on the phase of gravitational collapse of low-mass dense cores, cradles of sunlike stars. We summarize recent analytic work and numerical simulations showing that a substantial level of magnetic field diffusion at high densities has to occur in order to form rotationally supported disks. Furthermore, newly formed accretion disks are threaded by the magnetic field dragged from the parent core during the gravitational collapse. These disks are expected to rotate with a sub-Keplerian speed because they are partially supported by magnetic tension against the gravity of the central star. We discuss how sub-Keplerian rotation makes it difficult to eject disk winds and accelerates the process of planet migration. Moreover, magnetic fields modify the Toomre criterion for gravitational instability via two opposing effects: magnetic tension and pressure increase the disk local stability, but sub-Keplerian rotation makes the disk more unstable. In general, magnetized disks are more stable than their nonmagnetic counterparts; thus, they can be more massive and less prone to the formation of giant planets by gravitational instability.
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