While Mod Support has been available on Xbox One since May, PS4 players are still waiting the arrival of this feature. Unfortunatelly, it might still take a while as Bethesda confirmed that it's working with Sony to bring the feature to PS4, but that the process is still under evalution.
"We're working w/ith Sony on Fallout 4 Mod support for PS4," said Bethesda on Twitter. "The process is still under evaluation. As soon as we learn more, we will share news."
Mod Support had been due to be available in June, but Bethesda announced the delay after some problems with mods were found. Lack of sound file support and a storage limit capped at 900 MB are some of the issues that currently prevent the use of mods on PS4.