While Sony is steadfastly against any form of backwards compatibility on the PS4 (which doesn’t let users play games from the PS3 or PS1, and only allows users to rebuy older PS2 games from a limited catalog, even if they had bought them previously), it seems like that might change with the PS5. A new patent that Sony filed seems to reference backwards compatibility, suggesting that the feature may come in their next console.
This makes sense on some level- one of Sony’s reasons for moving to x86-64 architecture was, after all, to ensure continuity and easier transitions between generations, of which backwards compatibility would be a part. That said, this is only a patent filing, and it doesn’t even explicitly specify backward compatibility for games, so let’s not get ahead of ourselves here.
While Sony were among the pioneers of backwards compatibility on consoles (the PS2 was fully compatible with the PS1, and the PS3 with both), they have since given up on the idea- the PS3 eventually gave up on compatibility with PS2, and the Vita was only partially compatible with the PSP. The PS4 wasn’t backward compatible at all. If the PS5 is backward compatible with PS4, it will be the first Sony console in over a decade to have backward compatibility- here’s hoping.