Inside the Genesis they had the hardware for the Master System, which included the original Z80, the original sound chip. The Genesis graphics chip was evolved from the Master System and could work in Master System mode. You needed a cartridge adapater.
The other surprising thing is that you could actually run the Z80 in parallel with your 68000 when running a Genesis game. We used the Z80 as a sound co-processor running MIDI and playing sampled drums without bothering the 68000.
On the PS2 system's PS1 backwards compatibility this pattern is quite similar, not mentioned in the blog posts is that the IOP which acts as the PS2's sound co-processor contains an R3000 like the PS1 and it's underclocked to directly run the PS1 titles.
Apparently on later editions of the PS2 Slim they removed the R3000 based IOP and replaced it with a PowerPC microcontroller! It had to fully emulate the R3000 and the SPU as far as I know to fufill the IOP duties including the PS1 emulation.