With Amstrad's introduction of the Spectrum +3 in 1988, the venerable Speccy needed a DOS, or Disk Operating System.
The official DOS in the Spectrum +3 is called +3DOS, and is a modified version of Amstrad's PCWDOS for their PCW line, which provided those computers with a CP/M-compatible disk system. The rewrite of PCWDOS was undertaken by Cliff Lawson. It's held in one of the two new 16 KB ROM chips (not found on the +2 or earlier models). The +3 was the first Spectrum touted as being able to run CP/M software. To ensure this could happen, the new +3DOS would allow bank-switching of memory (CP/M requires RAM at the bottom of the address space) so that the ROM code could be 'paged-out' for another 16 KB of RAM.
IDEDOS came about as part of the Spectrum +3e project. The DOS in the +3e consisted of a combination of +3DOS and IDEDOS. The IDEDOS part was written by Garry Lancaster, and was designed to hook into the simple 8-bit IDE interface designed by Pera Putnik. Later versions of the +3e ROMs work not only with the 8-bit IDE interface, but also the 16-bit ZXATASP and ZXCF IDE interfaces.
A later DOS by Garry Lancaster which supports the ZXATASP and ZXCF IDE interfaces. Both of these are 16-bit IDE interfaces designed and developed by Sami Vehmaa. ZXATASP is designed for hard disks, and ZXCF is designed for Compact Flash cards.