Shush is the modern city built upon the ruins of ancient Susa which was an Elamite Capital (see also Elamite delegation in Persepolis).
Susa is mentioned in the bible as Shushan and Daniel (of lion's den fame) lived in Susa during the 6th Century B.C.E. His tomb is very popular with Iranians who come to offer up prayers there.
Susa was the Elamite capital in 1400 B.C.E. However the sparse ruins one can see today date from the Achaemenid Persian empire after Susa was conquered by Cyrus the Great in 540 B.C.E.