For Intel users
older and all CPUs support gerneric.
I7/I5/I3 7XX~6XX, Xeon 3XXX~7XXX and E7 (before v2): Nehalem; generic
I7/I5/I3 2XXX~3XXX, Xeon E3/E5/E7 (~v2): Nehalem, SandyBridge; AVX
I7/I5/I3 4XXX~5XXX, Xeon v3~v4: Nehalem, SandyBridge, Haswell; AVX, AVX2
I7/I5/I3 6XXX~8XXX, Xeon v5~v6: Nehalem, SandyBridge, Haswell, Skylake; AVX, AVX2
The release order is:
Intel Core > Nehalem > Westmere > Sandy Bridge > Ivy Bridge > Haswell (start using AVX2) > Broadwell > Skylake > Kaby Lake > Coffee Lake
Use CPU-Z to check what microarchitecture (code name) and instruction is your CPU using is the best way, because some CPU like i7-4930K do not support Haswell version.

For AMD users
The release order is:
K5~K10 > Fusion > Bulldozer/Bodcat > Piledriver > Jaguar > Steamroller/Puma > Excavator (start using AVX2) > Ryzen
Use CPU-Z to check what microarchitecture (code name) and instruction is your CPU using yourself, because there are too many models of that.
Bodcat, Jaguar, Puma are the same series.
Bulldozer, Piledriver, Steamroller, Excavator are the same series.