Chade-Meng Tan has two quite readable books on meditation: "Search Inside Yourself" and "Joy on Demand". He talks in both of them about concentrating on one's breath. Many other books on meditation mention the same anchor for meditation practice: the breath.
There are many books on the breath, breathing, healthier breathing, proper breathing. There are books on the medical specialty of pulmonology, medicine of the respiratory tract. Most of these books seem to be about dealing with lung disorders and disease.
Since the breath can be focused on and used in meditation and since breathing is essential to staying alive, I am again interested in the connections between breath and mindfulness, awareness of my mind's activities. I have been interested in these subjects and their connections before and haven't made any great strides toward understanding or any new practices. I have found two basic types of special breaths, diaphramatic and puffed-cheeks.
"Conscious Breathing" by Gay Hendricks, PhD seems to be mostly about diaphragmatic breathing, which is much deeper and further down the body that simple, shallow chest breathing. Hendricks makes strong claims that physical health and also better moods and mood control can be attained with more deep, slow breath, consciously using the diaphragm. He notes that greater explicit use of the lower part of the belly is unacceptable for some people, who fear looking like they have beer bellies, even just during deep, full breathing.
Dr. Alan Watkins has some videos on YouTube that, like the book by Hendricks, mention better control over emotions and faster return to normal states from high tension with deep breathing. If you use the search window on the main page of this blog http://fearfunandfiloz.blogspot.com/ to search out "breath", 'breathing" and Buteyko, the Russian breath scientist, you can find previous posts about breathing. It is difficult for me to untangle real benefits from loose claims but I may find something eventually. Much of the benefits are supposed to related to mental calm, a difficult area to test.