Basket-Hall Kazan holds a little over 7,000 people. The club grew out of the city's university sports system in 1991 — the name itself is a contraction of "University-Culture-Sport" — and for three seasons in the mid-1990s played as Unics-Lokomotiv before the shorter name came back for good.
Domestically, Unics spent years arriving second: runner-up in the Russian Championship in 2000–01, 2001–02, 2003–04 and 2006–07, with the Russian Cup filling the gap instead — won in 2002–03 after extra time against CSKA Moscow, then again in 2008–09 and 2013–14. Europe came earlier than the national title did. The club took the FIBA Europe League in 2003–04, beating Maroussi Athens, and followed it with the EuroCup in 2010–11, a 92–77 final win over Cajasol Sevilla in which Marko Popović was named Final Four MVP. A second EuroCup final, against Valencia in 2013–14, ended the other way, and a third appearance in the final followed in 2020–21.
The Russian Championship itself did not arrive until 2022–23, when Velimir Perasović's side paired it with the VTB United League title in the same season — the first time both had been won together. Jalen Reynolds was named the League's Best Sixth Man that year.
Alexey Shved signed in November 2025 and was handed the captaincy for the 2026–27 season — a CSKA-era EuroLeague champion and a former VTB League MVP.