What territories were captured by the Persians in Asia, what in Europe?

We are talking about the Achaemenid Persian Empire in the 5th-4th centuries BC. Persians in Europe captured or vassalized some lands:

North-east of modern Greece.
Thrace. Now it is Bulgaria and the European part of Turkey between Edirne and Istanbul.
Some islands of the Aegean Sea. From Rhodes in the south to Thassos in the north.

In Asia, they took control of lands from the northeastern coast of the Red Sea to the Indus River, Transcaucasia, the territory of modern Turkey, the east of the Arabian Peninsula and the land between the Persian Gulf in the south and the Aral Sea in the north.



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