+1
AMD has been pretty good about cross socket compatibility, but AM4 uses DDR4, and they offer no support for DDR3 so the old chips will not work. They did take some of their older APUs and make them available on AM4 though, the 9000 series of APUs (Not the FX-9000 CPUs)
AM2 -> AM2+ and AM2+ -> AM3 was pretty common, but with caveats. Usually the HyperTransport speed would be lower the older you went back. So while you could drop AM3 cpus into AM2+ sockets, they would be slightly slower. And there was a big distinction between CPUs that supported DDR2 vs DDR3, so they released AM2+ compatible versions of AM3 chips to fill the gap.