Is the Caspian Sea in Europe or Asia?

The Caspian sea is found mainly in Asia. These countries include: Azerbaijan , Kazakhstan , and Turkmenistan, as well as parts of Russia and Iran.

If you look at the traditional border between Europe and Asia it is formed by the Ural Mountains and the Ural River. Therefore the Russian part of the Caspian Sea shore is in Europe. This is also the case with the Kazakh part that lies west of the Ural River. The rest of the sea shore in Kazakhstan, Azerbaijan, Turkmenistan and Iran is in Asia.

http://www.worldatlas.com/aatlas/infopage/caspiansea.htm

The traditional border between Europe and Asia also follows the Caucasus Mountains.
This means that the area in (and north of) the Caucasus belonging to the Russian federation is in Europe, while the area south of the border (Georgia and Azerbaijan) is in Asia.

https://www.reference.com/geography/mountain-range-separates-europe-asia-8d54c44a75952c73

The Caspian Sea is located between Europe and Asia. It is bounded to the northeast by Kazakhstan, to the northwest by Russia, to the west by Azerbaijan, to the south by Iran, and to the southeast by Turkmenistan.

https://en.wikipedia.org/wiki/Caspian_Sea