The primary X-ray emission in AGN is believed to be produced by Comptonization of optical/UV disk photons scattered up to the X-ray band by a hot corona located above the accretion disk. The emitted spectrum is, at the first order, a power-law with a high-energy cutoff, where the photon index and the cutoff energy are directly related to the temperature and to the optical depth of the plasma of hot electrons responsible for the inverse Compton scatteringTo investigate the physical properties of the corona and provide constraints on its parameters, we have studied the broad band spectra of a sample of local Seyfert galaxies observed with NuSTAR (in coordination with XMM-Newton, Suzaku or Swift). We will discuss the general properties of the sample, and show a few particularly interesting cases.