Mula Mustafe Bašeskije Street stretches from the main square in Baščaršija to Vječna Vatra, where it runs into Titova St.
Dating back to the Ottoman period, it used to be divided into several different sections: Ćemaluša, Za Banjom (Gazi Husrev Bey’s Hamam St.) and Gornja Varoš (Varoš).
Between 1914 and 1946 it had many different names: until 1919, part of it was called Vojvotkinje So je and another section was called Potiorekova; and from 1919 to 1941 the entire street was named after Aleksandar Karađorđević, first as Prijestolonasljednika Aleksandra Street, then as Kralja Aleksandra Street.
From 1941 to 1945 it was called Dra Ante Pavelića and then renamed Maršala Tita Street.
It received its current name in 1993 in honor of the famous Sarajevo chronicler and poet, Mula Mustafa Ševki Bašeskija (1731-1808). His Chronicle, which was written in Ottoman Turkish, provides a valuable glimpse of Sarajevo life during the second half of the 18th century.