Most 1980's home computers that had disk drive options used an internal disk controller with external drives attached under the control of the computer. The BBC, Spectrum and Apple were like this. Commodore and Atari disk drives are rather different. They are in fact computers in their own right, connected via a serial bus. So in modern terms, more like a network server that a USB hard drive.
X cables over the years. This is quite a nice little XA1541V2 board I picked up this one on ebay a few years ago. It has transistor drivers to boost the drive capabilities. The only problem with these is the lack of a parallel port on modern computers. I have an old XP laptop I keep for this sort of task, which has built in parallel and serial ports.
xum1541 is a USB to 1541 interface, and ZoomFloppy is an nice implementation of that. I don't know if these are still current, these seem to date to 2011. All the information is there, so I set about building one.
opencbm. These are still there, and still work. This is cbmctrl, which is used for sending commands to the drive such as reset, status and directory.