  We review the physical phenomena that arise when quantum mechanical energy
levels are modulated in time. The dynamics resulting from changes in the
transition frequency is a problem studied since the early days of quantum
mechanics. It has been of constant interest both experimentally and
theoretically since, with the simple two-state model providing an inexhaustible
source of novel concepts. When the transition frequency of a quantum system is
modulated, several phenomena can be observed, such as
Landau-Zener-St\"uckelberg-Majorana interference, motional averaging and
narrowing, and the formation of dressed states with the presence of sidebands
in the spectrum. Adiabatic changes result in the accumulation of geometric
phases, which can be used to create topological states. In recent years, an
exquisite experimental control in the time domain was gained through the
parameters entering the Hamiltonian, and high-fidelity readout schemes allowed
the state of the system to be monitored non-destructively. These developments
were made in the field of quantum devices, especially in superconducting
qubits, as a well as in atomic physics, in particular in ultracold gases. As a
result of these advances, it became possible to demonstrate many of the
fundamental effects that arise in a quantum system when its transition
frequencies are modulated. The purpose of this review is to present some of
these developments, from two-state atoms and harmonic oscillators to multilevel
and many-particle systems.
