Pranayama by Baba Ramdev
Baba Ramdev (born 1974) is an iconic figure in India who has rejuvenated interest in Yoga and Pranayama among the Indian masses. In the videos below, Baba Ramdev gives extensive instructions in 'shuddha Hindi', which is music to my ears :)

English speakers: YouTube Playlist of Pranayama Videos in English is available. The instructions in Hindi videos are more spiritual and vivid (how to breathe, what to think, where to focus, what benefits to expect).

Personal Notes: Below each video, I have jotted down brief personal notes for myself. I have not transcribed all sentences in the video. You should watch these videos yourself and make your own notes, especially if you have health problems. Baba Ramdev actually gives lots of instructions. I've found it difficult to remember them all. So I watch these videos every few weeks. Every time, I learn something new.

Western Research: See Wikipedia article for some references. It appears that there is far more research on meditation than on pranayama.