By the 1980s, Grobari were one of the largest and most organized fan groups in SFR Yugoslavia and began out-marching to all of Partizan's matches across the country and Europe.

Because of their expressed hooliganism toward other club's supporters in those times, fans who represented the core of the Grobari firm were often referred to as a "punishment expedition".

In the 1990s, the unique, yet unofficial mascot of mostly all Grobari fan groups was an angry looking bulldog, but in the last few years it has been a gravedigger standing next to his shovel.

Revolted by Partizan being eliminated from the Champions League qualifications, followed by elimination from the first round of the UEFA cup and from the national cup competition by a third division team, as well as poor results in the domestic league (all at the start of the 2005–06 season), Grobari declared a complete boycott of all Partizan football club matches.

Grobari repeated the massive gathering and reiterated their demands in October 2005 in front of the national theatre in downtown Belgrade where Partizan's officials were celebrating the club's 60th anniversary.

A faction of fans calling themselves Zabranjeni (The Forbidden) accused the club board of denying them entrance to the stadium.

Current leading groups on the south stand of Grobari are: Shadows, Anti Romi, Principi, Još Neko Kopa and Partizan Offender.

[4][5] They are also known for their nationalist paroles, and often show flags of Serbia and notable pictures of 90s warlord Ratko Mladić on Partizan games.