  I describe the Time-Dependent Superfluid Local Density Approximation, which
is an adiabatic extension of the Density Functional Theory to superfluid Fermi
systems and their real-time dynamics. This new theoretical framework has been
applied to describe a number of phenomena in cold atomic gases and nuclear
collective motion: excitation of the Higgs modes in strongly interacting Fermi
superfluids, generation of quantized vortices, crossing and reconnection of
vortices, excitation of the superflow at velocities above the critical
velocity, excitation of quantum shock waves and domain walls in the collisions
of superfluid atomic clouds, excitation of collective states in nuclei.
