This is an incredibly difficult question to answer, because ancient history is nearly lost to us. To be honest, not many people know anything about Indo-European people. All theories are educated conjectures that have many critics. Moreover, when we come to the life of the Ancient Near East, the same problems emerge - the lack of reliable information.
In light of these points, there seems to have been a massive change in society around 900 BC in Greece and the Ancient Near East. The great civilizations of the Minoans in Crete seems to be destroyed. The more plausible explanation is the migration of Indo-Europeans. Similarly, when we move to the Ancient Near East, we see the presence of the Hittites, the earliest Indo-Europeans that we know of. They seemed to have be the greatest power during the Bronze and Iron ages.
Their impact can be seen in several areas. First, they brought their language. To be sure cuneiform did not persist as a language, but at least they wrote, which cannot be underestimated. They also influenced warfare. To the best of my knowledge, they were the first to introduce chariots. Finally, their religion influenced the Ancient Near East.