Majority of flights to Kazakhstan land in the Almaty airport.
It's geographical location right in the heart of the Eurasian continent attracts many Central Asian and Silk Road travellers, naturally stimulating the interest of the dominant world air passenger and cargo carriers.
You can see the rising popularity of the Almaty international airport from the amount of new Almaty flights appearing on their schedules lately.
Here is the map with world international airports worldwide, from where you can have direct International and CIS flights to Amaty, Kazakhstan.