  When two operators $A$ and $B$ do not commute, the calculation of the
exponential operator $e^{A+B}$ is a difficult and crucial problem. The
applications are vast and diversified: to name but a few examples, quantum
evolutions, product formulas, quantum control, Zeno effect. The latter are of
great interest in quantum applications and quantum technologies. We present
here a historical survey of results and techniques, and discuss differences and
similarities. We also highlight the link with the strong coupling regime, via
the adiabatic theorem, and contend that the "pulsed" and "continuous"
formulations differ only in the order by which two limits are taken, and are
but two faces of the same coin.
