The Sanhedrin can trace its lineage back to its formation in the time of Moses. Moses was the head of the first sanhedrin. The sanhedrin ceased to exist some time after the destruction of the Second Temple.
One of the requirements of being a member of the Sanhedrin is having received semicha. Semicha had to be transmitted in an unbroken line extending back to Moses. However, as part of their subjugation of the Jews, the authorities outlawed the transmission of semicha.
The Sanhedrin as a body had powers that other courts did not have. As such, they were the only ones who could try the king, extend the boundaries of the Temple and Jerusalem, and were the ones to whom all questions of law were finally put.
The Jewish anticipation for the arrival of the Messiah includes the reconstitution of this body of sages.