  We point out the universal presence of the excitonic superexchange in
spin-orbit-coupled Mott insulators. It is observed that, the restriction to the
lowest spin-orbit-entangled "$J$" states may sometimes be insufficient to
characterize the microscopic physics, and the virtual excitonic processes via
the upper "$J$" states provide an important correction to the superexchange. We
illustrate this excitonic superexchange from a two-dimensional $5d$ iridate
Sr$_2$IrO$_4$ and explain its physical consequences such as the orbital-like
coupling to the external magnetic flux and the nonlinear magnetic
susceptibility. The universal presence of the excitonic superexchange in other
spin-orbit-coupled Mott insulators such as $3d$ Co-based Kitaev magnets and
even $f$ electron rare-earth magnets is further discussed.
