Vassal states were areas under persian military and financial dominon of a larger more powerful state.
Persian Vassal states include Libya, sardis babylon, Syria, Jerusalem, Lesbos, chias, sarvos, cyrene, egypt, india, phonecia, Thrace, Ionia, scyths, caria and the Aegean islands.
The vassal states were governed by a satrap, who was ussually family member of the king or a noble. They paid taxs in the form of tributes to the king.
That all i know i guess there is more to know