A popular approximation to the Casida equations is the Tamm-Dancoff approximation (TDA), which simplifies the algebra and associated algorithms to obtain the electronic excitations, yet it typically yields electronic excitations close to those obtained by TD-DFT. Unfortunately, TD-DFT on the basis of popular exchange correlation functionals suffers accuracy limitations which are most evident in the failure to correctly describe Rydberg and charge transfer (CT) states. These drawbacks can usually be overcome by range-separated hybrid (RSH) functionals, which employ a large amount of HF exchange at large electronelectron distances and, therefore, reflect the correct asymptotic exchange potential. TD-DFT in numerous variants has been applied to PPs, and in the following we are summarizing the state of the art as found in the current literature: