Named for the basic color of the figures, this form of pottery is called red-figure.
The style of painting continued to evolve. Euphronios is one of the most important of the painters from the early red-figure period. Simple style came first, often focusing on Dionysus. It grew more complex as it became more widely used, with techniques spreading throughout the Greek world.
Tip: Of the two, black-figure came first, but if you're looking at a large collection at a museum, it's easy to forget. Remember that whatever color the vase appears, it's still clay, and therefore reddish: clay=red. It is more obvious to paint black figures on a red substrate than it is to paint negative space, so the red figures are more evolved. I usually forget, anyway, so I just check the dates of a couple, and go from there.
For more information, see: "Attic Red-Figured and White-Ground Pottery," Mary B. Moore. The Athenian Agora, Vol. 30 (1997).