I will discuss the structure and emission of models of magnetized accretion disks irradiated by the central star, expected to form as a result of the gravitational collapse of magnetized rotating dense cores. The mass-to-flux ratio is a critical parameter for their structure. Recently, magnetic fields have been observed at the scale of disks. Thus, in the near future, this parameter will be determined observationally with radio interferometers like ALMA and VLA. I will also discuss the modeling of millimeter observations of the disk around the young star HL Tau.