It was my understanding that some yogurt contains live cultures. I learned to look for the Live Cultures emblem on yogurt containers. You can read more about it here
Live Culture, but to paraphrase, all yogurt is made with pasteurized milk, after which the cultures are added. That is why it is allowed. Some yogurts are heat treated afterwards, which kills the cultures, but some are not. There is a list on that site of companies approved to use the Live Cultures seal.
I prefer the Greek yogurts that have not cut the corner and added thickening ingredients instead of draining their yogurts. Fage and Chobani are two still making their yogurts the old-fashioned way. Although Fage is not listed on the site as having live active cultures, it and Chobani do. I have made yogurt from adding a bit of Fage, but I can't match their taste that I like.