Over the past almost 40 years, time-dependent density functional theory (TDDFT) has enabled the calculation of electronic spectra and dynamics in systems that would have been otherwise out of reach to treat quantum-mechanically. While ground-state density functional theory (DFT) is the mainstay of electronic structure, being itself the most widely-used method for materials and molecules as well as the starting point of almost all other treatments of materials, it does not give excitations, or more generally the response to a time-dependent external field whether weak or strong. In the vast majority of cases, TDDFT is applied in the linear response regime, where weak perturbations of the ground state formulated in the frequency domain provide excitation spectra and oscillator strengths; the favorable system-size scaling of TDDFT has been further enhanced with the use of embedding methods or stochastic orbitals. A key element in these calculations is the exchange-correlation potential, which is unknown and needs to be approximated. Moreover, exact exchange-correlation potential has memory-dependence. Ever since the early days of TDDFT, researchers have been striving to build approximations that include this memory-dependence. In this work, Prof. Neepa T. Maitra et al. from the Department of Physics, Rutgers University, reviewed these efforts and their successes, reasons for why they are not widely used, and discussed prospects of future developments. Before doing so, the authors demonstrated, using an exactly-solvable model system, the implications of memory-dependence for both dynamics and excitations, and discussed some exact conditions related to memory dependence. They indicated that the search for an accurate and practical non-adiabatic approximation is a challenging one. The search is on-going and creative: several recent new directions have been proposed for time-dependent functional development which are still at a very preliminary stage, including coupling-constant integral transforms, re-casting TDDFT using the second-time-derivative of the density as basic variable, and extensions of the connector theory approach to the time-domain. Whether one of these will yield an elixir remains to be seen, but even if not, they reveal interesting physics about the dynamics of electron correlation.