This is azalea leaf gall, a fungus disease common on evergreen azaleas, especially in wetter than normal weather. Pick or cut them off by hand and dispose of them. Treatment with a fungicide is not necessary and the disease is only very rarely a threat to the overall health of the plant.

Agree, and I've got some on an azalea hedge I inherited with this house. A clipped hedge isn't quite my style, and not one of azalea ;0) I'm just handpicking the galls, disposing of them. To spray with a fungicide, application must begin just at bud break, your plants are past that this year. Then continue every couple of weeks until foliage matures. That's a lot of spraying for a problem that doesn't prove that noticeable or cause particular damage. And with my own, the deer browse lightly on the hedge just about year round. They aren't invited and I do what I can to discourage them, but I have no reason to want to make them sick either.