VME is primarily a bus standard for computer systems. VERSAbus Microprocessor Equipment, or something like that.
Physically it used Eurocard-sized circuit boards (3U, 6U or 9U sized) and it had a card cage to hold these boards. You could have a microprocessor board, memory cards, I/O cards, additional processors etc from different manufacturers all sharing a common signalling and memory mapping convention. It's about 20-25 years old now, but incredibly versatile and successful in its field.
As well as the makes mentioned already, I know Texas Instruments had a VME-based PLC system, the 575, which was programmed using not computer languages but standard ladder with Tisoft. It used TI's own 505-series I/O (which surprise, surprise was single-height 3U Eurocard sized boards!) but could also accommodate other processors in the rack for things that PLCs typically weren't too good at : vision systems, high-speed motion and positioning control servo-systems etc
Unfortunately, this was in the days before IEC-61131 so forget the language compatibility for the 575. All in all a great piece of kit for its day.
regards
Ken M.