The history of Kazakhstan runs from Bronze Age herders on the steppe to a modern republic that is barely thirty-five years old. Between those points sit the Saka horse warriors, the Silk Road cities of the Syr Darya, the Mongol conquest, a Kazakh Khanate founded in 1465, two centuries of Russian rule, seven decades of Soviet rule, and independence declared on 16 December 1991.
The short version
If you want the history of Kazakhstan in a paragraph: nomadic confederations herded and fought across this steppe for three thousand years while caravan cities grew along its southern rivers. Genghis Khan swept through in the 1220s and the region became part of the Mongol empire, then of its successor khanates. In 1465 two sultans broke away to found the Kazakh Khanate, which split into three zhuz — the Great, Middle and Little Hordes. Facing Dzungar invasion, those hordes accepted Russian protection from 1731 onward, and protection became annexation. The Soviet period brought forced settlement and a catastrophic famine in the early 1930s, then wartime deportations, the Virgin Lands campaign, the Semipalatinsk nuclear test site and the Baikonur cosmodrome. Kazakhstan was the last Soviet republic to declare independence, on 16 December 1991.
When did Kazakhstan become a country?
It depends which founding you mean. As an independent state, Kazakhstan dates from 16 December 1991 — the last of the fifteen Soviet republics to declare independence, nine days before the USSR itself was dissolved. As a distinct Kazakh polity, the date usually given is 1465, when Sultans Zhanibek and Kerey led their followers away from the Uzbek Khanate into the Zhetysu valleys and founded the Kazakh Khanate; Kazakhstan marked the 550th anniversary of that event in 2015. And as a named territorial unit, the Kazakh ASSR was created within Soviet Russia in 1920 and became the Kazakh SSR in 1936.