Approaches based on TDDFT are well established to calculate excited state properties. However, when dealing with periodic systems, the routine usage of hybrid functionals is often hindered due to the increased computational costs in comparison to GGA functionals. We presented two approximate schemes based on the ADMM and sTDA approaches with the goal to reach hybrid functional accuracy at reduced cost. Benchmark results for molecular and periodic systems show that the two methods can indeed reach the required accuracy for excited-state properties and allow for an efficient calculation of many excited states. First, the implemented ADMM-approximated hybrid functional kernel leads to a speed-up of at least one order of magnitude in comparison to conventional hybrid functional TDDFT and thus enables practical calculations on large systems of hundreds of atoms at moderate cost. Timings could be further improved by accelerating the evaluation of the exact exchange integrals using either standard resolution-of-the-identity approaches or semi-numerical integration. In comparison to inherent methodological errors of TDDFT due to the chosen density functional, the loss in accuracy for ADMM-approximated kernels is minor when choosing auxiliary basis sets of at least triple-zeta size. ADMM / TZVP+tzp MADs in excited-state bond lengths are in the range of 0.2 pm and corresponding vertical and adiabatic excitation and fluorescence energies are off by 0.02 to 0.04 eV. In contrast, conventional PBE0 / TZVP bond lengths and adiabatic excitation energies show MADs of 1.0 pm and 0.4 eV with respect to EOM-CCSD / def2-TZVPP reference data. The given ADMM accuracy estimate represents a lower limit that was found to be reliable when choosing the simplest ADMM variant based on basis projection in combination with a triple-zeta auxiliary basis. It could be further improved by either adding an exchange density functional correction to compensate the incompleteness error or -regarding the perpendicular methodological error -by switching to more sophisticated ADMM schemes with the latter however increasing the complexity of implementation. The semi-empirical sTDA method is particularly useful when aiming for broad-band absorption or emission spectra and efficient pre-screening of large-scale test sets. An order of magnitude speedup was achieved with sTDA in comparison to ADMM when computing spectra over the lowest 500 excitation energies, with resulting timings being in the range of minutes rather than hours. Due to the reduced amount of ERIs, the sTDA kernel also accelerates timings by a factor of two for each ES geometry optimization cycle. However, an increased number of optimization steps can lead to total timings comparable to ADMM. We expect that further savings could be achieved when optimizing the current sTDA ES gradient implementation as well as when choosing a semi-empirical GS reference. In comparison to hybrid functional kernels, sTDA MADs in excited-state bond lengths with respect to EOM-CCSD reference results are only slightly increased to 1.1 pm.