PPSSPP

The rare emulator that is essentially finished.

What it does

PPSSPP runs PSP titles at up to 10× the handheld’s native resolution, with texture scaling and replacement packs, save states, controller mapping, and post-processing shaders. Compatibility is very high and performance is not a concern on any Apple Silicon Mac — it was written to run acceptably on phones a decade ago.

It reads ISO, CSO and extracted PSP folders directly, and needs no BIOS at all.

Notes

No BIOS requirement is the practical difference from every other console emulator here: supply a game and it runs.
The Vulkan backend via MoltenVK is the fast path on macOS; the OpenGL one is the fallback for older games with shader issues.
Emulation is lawful. The games are yours to rip from UMDs you own.

Alternative to

Alternative	Type	Trade-off
Vita3K	Open source	The PS Vita, considerably less complete
RetroArch	Open source	PPSSPP as a core, with shaders and run-ahead around it
OpenEmu	Open source	PSP via the experimental core set, inside a library
A PSP	Paid	The original screen, and a UMD drive