One-dimensional radiative transfer (RT) calculations suggested that the scattering polarization profiles of the Hα line are very sensitive to the strength and structure of the chromospheric magnetic field. Here we present unprecedented spectropolarimetric observations of the Hα line obtained with ZIMPOL-3 at IRSOL. The linear polarization profiles show a rich variety of shapes and amplitudes, as well as an interesting spatial variability. We confront them with the theoretical scattering polarization profiles we have obtained by solving the complex RT problem of the Hα polarization in a 3D model from MHD simulations, highlighting the impact produced by the model's magnetic and velocity field. This investigation reveals the great interest of the Hα polarization in the present new era of large-aperture solar telescopes.