Indo-European migrations were the migrations of pastoral peoples speaking the Proto-Indo-European language, who departed from the Yamnaya and related cultures in the Pontic–Caspian steppe, starting at c. 4000 BCE. They spread throughout Europe and Asia, forming new cultures with the people they met on their way, including the Corded Ware culture in Northern Europe and the Vedic culture in India.

Modern knowledge of these migrations is based on data from (a) linguistics, (b)archaeology, (c) anthropology and (d) genetics.

a) Linguistics describes the similarities between various languages, and the linguistic laws at play in the changes in those languages.

b/c) Archaeological data, describes the spread of the Proto-Indo-European language and culture in several stages from the Proto-Indo-European Eurasian homeland in the Pontic–Caspian steppe, into Western Europe and Central and South Asia, by migrations, and by language shift through elite-recruitment as described by anthropological research.

d) Recent genetic research has a growing contribution to the understanding of the historical relations between various historical cultures.

The Indo-European languages and cultures spread in various stages.

Early migrations from c. 4200–3000 BCE brought archaic proto-Indo-European into:

1) the lower Danube valley,
2) Anatolia, and the
3) Altai region

4) Pre-Celtic and pre-Italic probably spread into Europe after new migrations into the Danube Valley,

5) While pre-Germanic and pre-Balto-Slavic developed east of the Carpathian mountains, at present-day Ukraine, moving north and spreading with the Corded Ware culture in Middle Europe (third millennium BCE).

6) The Indo-Iranian language and culture emerged at the Sintashta culture (c. 2100–1800 BCE), at the eastern border of the Yamna horizon and the Corded ware culture,growing into the Andronovo culture (c. 1800–800 BCE).

7) Indo-Aryans moved into the Bactria–Margiana Archaeological Complex (c. 2300–1700 BCE) and spread to the Levant (Mitanni), northern India (Vedic people, c. 1500 BCE), and China (Wusun).

8) The Iranian languages spread throughout the steppes with the Scyths and into Iran with the Medes, Parthians and Persians from ca. 800 BCE.

(Straight from Wikipedia. This isn’t controversial. It’s just how it is.)