  The adiabatic approximation in time-dependent density functional theory
(TDDFT) yields reliable excitation spectra with great efficiency in many cases,
but fundamentally fails for states of double excitation character. We discuss
how double-excitations are at the root of some of the most challenging problems
for TDDFT today. We then present new results for (i) the calculation of
autoionizing resonances in the helium atom, (ii) understanding the nature of
the double excitations appearing in the quadratic response function, and (iii)
retrieving double-excitations through a real-time semiclassical approach to
correlation in a model quantum dot.
