Time-dependent density-functional theory (TDDFT) is a formally exact framework for the dynamics of interacting many-electron systems, and provides computationally convenient alternatives to the time-dependent many-body Schroedinger equation. Today, most applications of TDDFT are in the linear regime for the calculation of excitation spectra of molecules. However, TDDFT is also ideally suited for nonlinear phenomena in strongly driven systems. This talk gives an overview of such applications of TDDFT, with an emphasis on phenomena that are relevant in the context of warm dense matter. We will discuss the time and intensity scales where TDDFT is applicable, and the performance, predictive capabilities, and challenges of TDDFT with present-day approximations and computer codes. Examples will include atoms, molecules, and solids in strong fields such as those produced in the new generations of advanced light sources.
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