Taking over the Median empire meant taking over the Median countries, i.e. Armenia, Cappadocia, Parthia, Drangiana, Aria, Chorasmia, and Bactria. In 547, Cyrus added Lydia to his possessions, an empire that had among its vazals Greeks and Carians. Eight years later, the Persian ruler conquered Babylon (October 539). The Babylonian empire had been large, and Cyrus now became ruler of Syria and Palestina as well. He allowed the Jews, who were exiled to Babylon, to return home.
The Greek-Roman author Arrian tells us in his book about Alexander the Great (the Anabasis) that Cyrus founded a frontier town in Sogdiana; there is no reason to dount this statement. The Greeks called this town Cyropolis ("Cyrus' town") or Cyreschata (a pun on the name of the king and the word "far away"); both names seem renderings of Kurushkatha, "Cyrus' town". Another story by Arrian deals with Cyrus' expedition to India; probably, this stories is also accurate, but we cannot be completely certain. Cyrus' latest expedition took him to modern Kirgizistan, where he had fought against a nomadic tribe called Massagetes. The news of his death in battle reached Babylon in December 530, where letters were dated "first year of the reign of Cambyses".
Cyrus' capital was Pasargadae, where inscriptions in his palace state "Cyrus the Great King, an Achaemenian." His tomb (picture) was venerated by later rulers, a.o. the Macedonian king Alexander the Great.
The most important sources documenting the reign of Cyrus are the contemporary Chronicle of Nabonidus and the first book of the Histories by the Greek researcher Herodotus. All texts related to the fall of Babylon can be found here. The book known as Education of Cyrus by the Greek writer Xenophon is almost useless.