This Tuesday, December 18th, is the fast of Asara B’Teves. Asara B'Teves was the tragic day on which Nebuchadnezzar laid siege to Yerushalayim.
During Shacharis, the Sheliach Tzibbur says Aneinu. After Chazaras Hashatz, the following are said: Selichos, Avinu Malkeinu, Tachanun, Krias HaTorah ("Vayechal Moshe").
During Mincha, the following are said: Krias HaTorah ("Vayechal Moshe"), Haftorah ("Dirshu Hashem,") Aneinu during Shemoneh Esrei, Birchas Kohanim. For nusach Ashkenaz, Sim Shalom replaces Shalom Rav. Avinu Malkeinu is recited after Shemoneh Esrei.