Short answers, pulled from the story.
Otto Schrader published a work in 1883 that first formulated the idea of steppe nomads as Proto-Indo-European speakers. German scholars Theodor Benfey and Karl Brugmann followed with arguments in 1869 and 1870 respectively.
Marija Gimbutas introduced the term Kurgan culture in 1956 within her book The Prehistory of Eastern Europe Part 1. She defined four successive periods starting with Kurgan I in the Dnieper-Volga region during the earlier half of the 4th millennium BC.
Samara and Seroglazovka cultures from the Copper Age existed alongside Kurgan II through III which covered the latter half of the 4th millennium BC. Yamnaya or Pit Grave culture emerged around 3000 BC across the entire steppe region while Corded Ware culture stretched from Rhine to Volga during 3000 to 2500 BC.
Modern DNA studies from the 21st century show specific Y-DNA haplogroups expanding into Europe and South Asia. Populations bearing distinct genetic signatures migrated from Pontic-Caspian steppe during third and second millennia BC confirming migratory patterns out of Pontic Steppe at relevant time.
David Anthony published The Horse, the Wheel and Language in 2007 describing his revised steppe theory because he considered term Kurgan culture imprecise enough to be useless for modern research purposes. He used core Yamnaya culture and its relationship with other cultures as points of reference instead.