Achereshki is located on the left bank of the Gums River. It is 17 kilometres (11 mi) south-east of the town of Kurchaloy and is 57 kilometres (35 mi) south-east of the city of Grozny.
The exact date of Achereshki being founded is unknown, but it is presumed that it was approximately in 1810.
In 1944, after the genocide and deportation of the Chechen and Ingush people and the Chechen-Ingush ASSR was abolished, the village of Regita was renamed to Antsukh, and settled by Avars from the Georgian SSR.[4]
In 1958, after the Vaynakh people returned and the Chechen-Ingush ASSR was restored, the village regained its old Chechen name, Achereshki. The Avar people were resettled back to the Georgian SSR, in the village of Tivi (Gurgin-Rosu).