Greenmarket Square was built way back in 1696 and at the time was (disgracefully) used as a slave market and later a vegetable market. In the 1950s it was apparently (though I wasn't around to verify this) used as a parking lot, and only in the 1980s was it converted into a craft and flea market for informal traders.
The area is super-safe during the day, though I'd keep a wary eye open for suspicious-looking people at night. This said, I felt safe enough to whip out my camera and take a few photos of the deserted market area.