  Within the broad class of multiferroics (compounds showing a coexistence of
magnetism and ferroelectricity), we focus on the subclass of "improper
electronic ferroelectrics", i.e. correlated materials where electronic degrees
of freedom (such as spin, charge or orbital) drive ferroelectricity. In
particular, in spin-induced ferroelectrics, there is not only a {\em
coexistence} of the two intriguing magnetic and dipolar orders; rather, there
is such an intimate link that one drives the other, suggesting a giant
magnetoelectric coupling. Via first-principles approaches based on density
functional theory, we review the microscopic mechanisms at the basis of
multiferroicity in several compounds, ranging from transition metal oxides to
organic multiferroics (MFs) to organic-inorganic hybrids (i.e. metal-organic
frameworks, MOFs)
