Stepanović made his name with OFK Beograd where he was a right back fixture for 11 years between 1962 and 1973, before moving on to Red Star Belgrade for three seasons until 1976.

Stepanović is a former Yugoslav international, and used to be a favourite of national team head coach Vujadin Boškov.

He made a managerial name for himself in Germany with Eintracht Frankfurt before taking over at Bayer Leverkusen, replacing Reinhard Saftig shortly before they won the 1993 DFB-Pokal Final.

He was idolized in the US and finally came to Columbus, Ohio, in 2002 to coach the youth soccer club Blast FC.

In December 2006, Stepanović was a short-list candidate for the Bosnia-Herzegovina national team coaching spot, but the job went to Fuad Muzurović instead.