  We review the current theoretical models of the inward advection of the large
scale external magnetic fields in accretion discs. The most plausible theories
for launching astrophysical jets rely on strong magnetic fields at the inner
parts of the host accretion disks. An internal dynamo can in principle generate
small scale magnetic fields in situ but generating a large scale field in a
disk seems a difficult task in the dynamo theories. In fact, as far as numerous
numerical experiments indicate, a dynamo-generated field in general would not
be coherent enough over the large length scales of order the disk's radius.
Instead, a large scale poloidal field dragged in from the environment, and
compressed by the accretion, provides a more promising possibility. The
difficulty in the latter picture, however, arises from the reconnection of the
radial field component across the mid-plane which annihilates the field faster
than it is dragged inward by the accretion. We review the different mechanisms
proposed to overcome these theoretical difficulties. In fact, it turns out,
that a combination of different effects, including magnetic buoyancy and
turbulent pumping, is responsible for the vertical transport of the field lines
toward the surface of the disk. The radial component of the poloidal field
vanishes at the mid-plane, which efficiently impedes reconnection, and grows
exponentially toward the surface where it can become much larger than the
vertical field component. This allows the poloidal field to be efficiently
advected to small radii until the allowed bending angle drops to of order
unity, and the field can drive a strong outflow.
