  Despite targets of many multiwavelength campaigns, the main physical
processes at work in AGN are still under debate. In particular the origin of
the radio emission and the mechanisms involved are among the open questions in
astrophysics. In the radio-loud AGN population the radio emission is linked to
the presence of bipolar outflows of relativistic jets. However, the large
majority of the AGN population do not form powerful highly-relativistic jets on
kpc scales and are characterized by radio luminosity up to 10^23 W/Hz at 1.4
GHz, challenging our knowledge on the physical processes at the basis of the
radio emission in radio-quiet objects. The main mechanisms proposed so far are
synchrotron radiation from mildly relativistic mini-jets, thermal
cyclo-synchrotron emission by low-efficiency accretion flow (like ADAF or
ADIOS), or thermal free-free emission from the X-ray heated corona or wind. The
difficulty in understanding the main mechanism involved is related to the
weakness of these objects, which precludes the study of non-local radio-quiet
AGN. Multifrequency, high-sensitivity radio observations are crucial to
constrain the nature of the power engine, and they may help in distinguishing
between the contribution from star formation and AGN activity. The advent of
the SKA, with its sub-arcsecond resolution and unprecedented sensitivity will
allow us to investigate these processes in radio-quiet AGN, even at high
redshift for the first time. Both the broad-band radio spectrum and the
polarization information will help us in disentangling between non-thermal and
thermal origin of the radio emission. The jump in sensitivity of a few order of
magnitudes at the (sub-)uJy level will enable us to detect radio emission from
a large number of radio-quiet AGN at high redshift, providing a fundamental
step in our understanding of their cosmological evolution. (Abridged)
