The Planck satellite has mapped the polarized microwave sky (from 30 GHz to 353 GHz) with unprecedented sensitivity and angular resolution. This wealth of data yields the first complete map of polarized thermal emission from dust in our own Galaxy, shedding new light on the formation of dense cold structures within which new stars and planetary systems are born, under the combined effects of gravity, turbulence and magnetic fields. We present a statistical analysis of this polarized emission from nearby molecular clouds, with an emphasis on the evolution of the maximum polarization fraction observed as a function of column density, and on the anti-correlation between the polarization fraction and the local dispersion of polarization angles. To interpret this data, numerical simulations of anisotropic MHD turbulence underline the essential role played by the topology of the interstellar magnetic field, in particular its large-scale component. As an extension to this work published in Planck Intermediate Results XX (A&A, 576, 105, 2015), the statistical properties of the random component of the interstellar magnetic field are explored using a toy model based on fractional Brownian motion (fBm) fields.