One important thing when learning throatsinging and overtone singing is to have recordings to listen to. Here, I list some of my favorite videos, recordings, and artists for you watch and be inspired by.
In Tuva, it is also common for people to learn very much by listening, and I have found both for myself and students I work with that listening to recordings greatly increase one's own ability to learn how to sing overtones or throatsing.
Huun-Huur-Tu - Live in Berkeley (2008)
In terms of modern Tuvan bands that tour Internationally, Huun-Huur-Tu may be the most widely known. Huun-Huur-Tu means (In Tuvan) the vertical separation of light rays often seen on the grassland just after sunrise or just before sunset". This is thought to be a metaphor for how the multi-pitch singing they do separates into distinct, audible notes, like separating rays of sunlight. (Musicballkan.com)
This nearly 1.5 hour recording is meticulous in capturing the essential power and beauty of Tuvan music as expressed by Huun-Huur-Tu. You can tell the producers of the show put a lot of very specific care into the recording of these phenomenal sounds. There was probably a very focused effort on the post-production side as well to really bring forth the sounds as clearly and beautifully as possible. If you have time, I highly recommend watching this all the way through at some point. It is quite the sound journey, you may find yourself even transported to the boundless grassland and mountain steppe of the land of Tuva.
For shorter viewing period. Here are two excerpts from the performance showcasing individual styles of Tuvan throatsinging.
Anna Maria Hefele - "Polyphonic Singing"
This is Anna Mariia Hefele. An Overtone singer from Austria. When this video first came out a lot of people were sending it to me saying she did the thing they heard me do. Anna does overtone singing from a western style, and has a very technical approach to singing overtone and harmonics. Her style differs from what is practiced in the Siberian regions and is referred to by most people as "Western Overtone Singing". Her harmonics are very pure and beautiful.
Alexander Glenfield - Seven Styles of Tuvan Throatsinging
Alexander Glenfield demonstrates a variety of style of Traditional Tuvan Throatsinging, cleverly recorded in what sounds like, and appears to be, a marble hallway. Glenfield is a music major who travelled around Tuva learning how to sing like the traditional styles. He is very good and has some additional videos breaking down the way the harmonic structure works in overtone singing, and how Tuvan throatsinging works in particular.
Here is a video of Shonchalai Oorjak-Choodu, who was part of a female Tuvan Throatsinging group, something pretty uncommon. This is a beautiful video of her singing outside in Tuva, with what I believe is some goats milk. As part of a traditional Tuvan ritual goat's milk is often used as an offering.