(Translation from Russian based on http://www.bonistika.net/library.php?id=478&par=3 and http://forum.fox-notes.ru/index.php?topic=225.0)
The Independent Republic of Tannu-Tuva was proclaimed at August 13, 1921 in Sug-Bazhy (now Kochetovo), a small village in Tuva. In the first constitution of Tannu-Tuvait was declared that all international affairs would be done by the Russian Federation (later USSR). In September, the 1921 government of the Russian Federation acknowledges the independence of Tannu-Tuva.
At that time many different banknotes were in circulation - mostly issues from the Russian Empire, Russian Federation, and China. At the end of 1992 or in the beginning of 1923 the goverment of Tannu-Tuva put into circulation old Russian Empire banknotes with an overprint on the reverse. The overprint consists of text in an old Mongolian language and three signatures - that of the Prime Minister, Minister of Finance, and the Government's Advisor on Finance.
In 1925 a treaty of friendship was signed between the USSR and Tannu-Tuva. By agreement between goverments of the USSR and Tannu-Tuva the currency of USSR was put into circulation in Tannu-Tuva. Between 1925 and 1929 all previously circulating banknotes were removed from circulation.
In December, 1933 the government of Tannu-Tuva issue a decree of exchanging USSR banknotes in circulation for same notes, but with a blue overprint. This overprint consists of new Tannu-Tuva emblem and text "circulation allowed only in Tannu-Tuva" (original text in Russian "Имеет хождение только в ТНР"). Notes with this overprint were created by "Goznak USSR" (the official money printer of USSR, original name in Russian "Гознак СССР"). The exchange of this paper money continue until June, 1934. A total amount of 1,742,600 roubles was exchanged to new banknotes with an overprint.
On January 1, 1936 USSR banknotes with overprint were replaced by a new national currency - the aksa (original name in Russian "акша"). Old notes were exchanged to new banknotes at an exchange rate of 1 rouble = 1 aksa. New aksa banknotes was printed by "Goznak USSR" for total amount of 2,000,000 aksa (1 aksa - 400,000 notes, 3 aksa - 200,000 notes, 5 aksa - 100,000 notes, 10 aksa - 30,000 notes, 25 aksa - 8,000 notes).
Banknotes of the first aksa issue was in circulation for about 6 years. In 1939, preparation of the second aksa issue was begun. On August 11, 1939 a goverment commitee approved the design of new banknotes. The new notes were printed by "Goznak USSR" and put into circulation on March 1, 1941. The new paper money had the same denominations - 1, 3, 5, 10, and 25 aksa. The exchange of first issue notes continued until September 1, 1941. After the exchange banknotes for a total amount of 1,981,248 aksa were collected by the National Bank of Tannu-Tuva. On October 5, 1941 they were all destroyed in the presense of a government commitee. So, the total amount of remaining banknotes of first aksa issue was 18,752 aksa, with the following counts of each denomination: 1 aksa - 4822 notes, 3 aksa - 1560 notes, 5 aksa - 1217 notes, 10 aksa - 224 notes, 25 aksa - 37 notes. All banknotes of the first issue are extremely rare, especially higher denominations.
On October 11, 1944 the Republic of Tannu-Tuva joined the USSR and became an autonomous district of the USSR. Since January 1, 1945 banknotes of the USSR were put in circulation on the territory of Tannu-Tuva. It was possible to exchange aksa notes of the second issue for USSR roubles until May 1, 1945. After that date, all remaining Tannu-Tuva banknotes were declared void.
All banknotes of Tannu-Tuva nominated in aksa are extremely rare, especially those of the first issue.
Most of overprinted banknotes of the Russian Empire (Pick #1-4) selling today are forgeries (probably more than 99% of such banknotes on the market). This is due to the fact that banknotes of the Russian Empire are still cheap and available in large quantities. It is very hard to tell if a banknote is original. There are only few tips to help identify forgery. First of all, the overprint was never put abverse (front side of the banknote), only on reverse (interesting that even illustration in the Standard Catalogue of World Paper Money for #p3 has an overprint on abverse, so it's definitely fake). The overprints were made with wood stamp using black mineral pigment with a visible green tone. Most of the forged overprints are plain black with fine lines, while those originally produced with the wooden stamp should be a bit blurry.