There was a public statement put out by Bethesda not long ago that the company and Sony hadn't been able to figure out mods on the console, and that it wouldn't be coming to Fallout 4 or the Skyrim Remaster.
Well, it seems things got worked out as Bethesda have now announced that mods are actually coming to both games. This should be available to Skyrim when it launches later this month and Fallout 4 will follow later.
There is a small catch though. As Bethesda put it:
Mods on PlayStation 4 will allow you to modify and create your own content by using our Creation Kit. You will not be able to upload external assets with your PlayStation 4 mods, but you will be able to use any assets that come with the game, as most mods do.
This means you probably shouldn't be expecting Macho Man Randy Savage dragons or redone textures, but if you want insane punching power, or 100 dragons, you could probably do that.