While Microsoft steals the show with their extensive backwards compatibility, this is still shrouded in mystery on the side of the competition. Fortunately, Sony changed this yesterday with an extensive explanation on the PlayStation blog. It turns out that the Japanese manufacturer also has its affairs in order, because ultimately more than 99% of the PlayStation 4 games can be played on the new generation. The list of unsupported games has only ten titles and none of them is one we cannot miss.
The good news is that you can use your current DualShock 4 controllers for the supported games, and you can bring your savegames with you in multiple ways. Both via USB and PlayStation Plus it is possible to transfer your saved data to your brand new PlayStation 5. Unfortunately, it is not possible to use your Dual Shock 4 controllers for PlayStation 5 games, so if you want to sit on the couch multiplay, then you will still have to invest in an extra Dual Sense.
For the full explanation, read the post on the PlayStation blog.