In the early part of the 20th century, archeologist Aurel Stein discovered manuscripts in northwestern China in a script that had been lost for centuries, in a language that which completely stunned the linguistic community.
The first surprise was that it was an Indo-European language. That wasn’t such a huge surprise, since the Greeks had come tromping through almost 1000 years earlier, Northwest China was along the Silk Route not far from the historically powerful Indo-European-speaking Farsi speakers and the Indo-European-speaking Sanskrit speakers.
The second surprise was that it wasn’t Greek or Greek-derived, nor Farsi or Farsi-derived, nor Sanskrit or Sanskrit-derived. It appeared that it had been in the area for an awfully long time, not that some e.g. Finns took a wrong turn somewhere in 500 BC; Tocharian was a completely novel language.
The third, and biggest surprise, is that its structure was closer to the -European side of the Indo-European languages than to the Indo- side, despite being geographically closer to the areas that spoke languages on the Indo- side.
Despite the language being clearly European-ish, the writing system is Asian: it is an abugida (with “a” as the implied vowel) clearly derived from Brahmi; most of the surviving (and found) documents in Tocharian were translations of Sanskrit Buddhist documents.
Tocharain script had extra decorations to denote aspiration and nasalization.