Early in the 20th century, manuscripts written in a Brahmi script dated to the 6th-8th centuries AD were found at sites surrounding the Tarim Basin in western China north of Tibet, along what was once the Silk Road. The language of these ancient manuscripts was unknown, but some of them lay side by side with Sanskrit manuscripts of the same era that recorded Buddhist texts once in common circulation in Central Asia. Later it was determined that some manuscripts in the hitherto-unknown language were translations of the Sanskrit texts alongside them. The new language, now deciphered, came to be known as Tocharian. Eventually, discoveries of many more manuscripts led to the identification of a second new language, closely related to the first; the two became known as Tocharian A (a.k.a. Turfanian for its more eastern locale around Turfan, or Agnean for an Indic god in Sanskrit texts), and Tocharian B (a.k.a. Kuchean for the more western discoveries around Kucha), but they are commonly referred to via the group designation Tocharian when distinction is irrelevant.
Tocharian proved to an Indo-European language, one however that was quite different from the neighboring Indic and Iranian languages; indeed, the linguistic world was amazed by the realization that Tocharian -- now the easternmost known Indo-European language -- was more like "western" than "eastern" Indo-European languages, thus disrupting what had come to be regarded as a geographic distinction.
As the manuscripts were more carefully dated, it turned out that Tocharian A was the older language, while Tocharian B was younger. Texts in Tocharian A were strictly Buddhist documents, while texts in Tocharian B included monastic and business letters, caravan passes, and graffiti. It seems that Tocharian A, by the time the surviving documents were written, may already have been extinct -- preserved [by Tocharian B speakers] for liturgical purposes much as Latin was preserved in medieval Europe.
More recent discoveries of numerous Caucasian mummies dating to as early as the 2nd millennium BC, in areas known to have been inhabited later by Tocharian speakers, have occasioned much controversy and speculation: were these Caucasians the ancestors of the Tocharians who later lived there? Weaving patterns in the Caucasians' clothing exhibit notable similarities to clothing found in areas of central Europe, though no connection has yet been proven.