Protoplanetary disks are expected to form as a result of the gravitational collapse of magnetized rotating dense cores. Analytic work and numerical simulations that show that a substantial level of magnetic field diffusion has to occur at high densities in order to form the observed rotationally supported disks. I will discuss the radial and vertical structure of magnetized accretion disks irradiated by the central star, expected to form in this process. The mass-to-flux ratio is a critical parameter that determines the structure and evolution of these disks. This ratio can be determined observationally in the near future with radio interferometers like the Atacama Large Millimeter Array in Chile.