What emulators? How is the transfer process? Do standard ROMs work on the iPhone?
As somebody who uses an old Raspberry Pi pretty much exclusively for gaming these days, to play SNES-era games, I'm fascinated -- but I don't know anything about gaming on an iPhone.
I side-load RetroArch. Currently loaded stuff I've got on it (the App Store version doesn't support some of these modules) is: Atari 7800, Bandai WonderSwan, CHIP-8, Commodore 64, Commodore Amiga, DOS, Vectrex, Handheld games, MAME, Intellivision, GBA, GBC, N64, NDS, NES, Pokemon Mini, SNES, Sega 32x, SMS, Genesis, Sega CD, Saturn, SG-1000, Neo Geo Pocket, Playstation, PS2 (requires JIT enablement) and PSP. Separately, I've got some stuff loaded in Dolphin for GameCube and Wii.
Standard ROMs work, both uncompressed and compressed with zip or 7z, compressed disc images work, CHDs work for some platforms, all can be loaded via iCloud, via local network share, via browser download or even via a thumb drive plugged into the phone.
The on-screen touch controls are customizable (size, location, sensitivity), and the emulators support most controllers.
Now, to get RetroArch set up well, it can be really painful. Thankfully, the default settings aren't that bad; if you've got RetroArch on another system, it's often easier to set everything up there and then copy the settings over to the iPhone.
Full listing of emulation cores for sideloaded RetroArch is too large for me to list right now, and includes modern MAME, which itself supports all sorts of computing hardware as well as arcade machines (yes, you can run a Macintosh Quadra 800 or a Mac Plus in MAME in RetroArch on an iPhone).