Since 2012 the club has been one of the strongest teams in Europe, having reached UEFA Futsal Cup semi-finals four times and winning it in 2012–13 and 2014–15 seasons.

Kairat also switched to the practice of attracting Brazilian coaches: Paulo Augusto, Faisal Saab, Jose Alesio, Barbosa, Kakau now Kaka.

[2] In the middle of 2005/06 season "Kairat" was involved in a scandal with the Karaganda team "Tulpar", withdrawn in February from the championship.

With the support of their fans, the Almaty team was as close as ever to reach the final, but again stopped one step away from him, losing with a score of 2:3.

Then, in the match for third place, "Kairat" repeated the achievement of a year before last and defeated (3-3 and 5-3 in a penalty shootout) Portuguese "Benfica", became the bronze medalist of the tournament.

[5] In the 2014/2015 season Almaty "Kairat" in Lisbon (Portugal) in the final beat Spanish "Barcelona" (3-2), and became a two-time winner of the UEFA Futsal Cup.