  We study the magnetic interactions in Mott-Hubbard systems with partially
filled $t_{2g}$-levels and with strong spin-orbit coupling. The latter
entangles the spin and orbital spaces, and leads to a rich variety of the low
energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass
model depending on the lattice geometry. This gives way to "engineer" in such
Mott insulators an exactly solvable spin model by Kitaev relevant for quantum
computation. We, finally, explain "weak" ferromagnetism, with an anomalously
large ferromagnetic moment, in Sr$_2$IrO$_4$.
