We illustrate the scope of Time Dependent Density Functional Theory (TDDFT) for strongly correlated (lattice) models out of equilibrium. Using the exact many body time evolution, we reverse engineer the exact exchange correlation (xc) potential v_{xc} for small Hubbard chains exposed to time-dependent fields. We introduce an adiabatic local density approximation (ALDA) to v_{xc} for the 1D Hubbard model and compare it to exact results, to gain insight about approximate xc potentials. We also provide some remarks on the v-representability for the 1D Hubbard model. Finally, we present some results from work in progress.