It's still very (very very very) early days for PS4 emulation, but it's slowly improving with shadPS4 version 0.4 seeing a release on October 31st,
The changelog is long, but it brings many changes like shader recompiler fixes, an auto-update feature, and compatibility for new games like Gravity Rush Remastered.
The team keeps a compatibility list, and there are currently 29 games that are considered playable with many more that boot into game (but might suffer from different issues that make them unplayable for now).
And since you are probably wondering: Bloodborne boots into game but still crashes instantly.
shadPS4 is not the only PS4 emulator currently in development, as there is also RPSCX but development here seems slower.
