Interesting new study done recently. Check out here and here. The first link is an article which will also direct you to the second link. Just use the second link if you want to go right to the explanation of what the breathing techniques are/do. The study is explained in a series of videos. I haven’t watched them all yet.
What I gathered so far is the breathing exercises aid in feeling like you have better control over asthma and don’t replace anything but, help enough with the more milder symptoms that you don’t have to use rescue inhaler and therefore preventer medicine quite as much. One video said it won’t help with asthma triggered by allergies.