FK Crvena zvezda plays its home matches at a stadium named after Rajko Mitić, the captain and striker who led the great generation of the 1950s. That side reached the European Cup semi-final in 1957, where it lost to Fiorentina, and the quarter-final in 1958, where it went out 5–4 on aggregate to Manchester United. In the second leg, played in Belgrade on 5 February 1958, Red Star came back from 3–0 down to draw 3–3, but United, who had won the first leg 2–1, went through. It was the last match played by the "Busby Babes", whose plane crashed in Munich on the return journey the following day.
The club was founded on 4 March 1945. It took over the stadium and the red and white kit of the defunct SK Jugoslavija, and the colours have remained its identity ever since. The present ground opened on 1 September 1963 on the site of the former Jugoslavija stadium, with a 2–1 win over Rijeka. It was renamed after Mitić (1922–2008) in 2014. Known to supporters as "Marakana", it hosted the 1973 European Cup final, in which Ajax beat Juventus 1–0.
Red Star's European record includes several other notable runs. In 1973–74 the club eliminated Liverpool in the second round of the European Cup, and in 1971 it reached another semi-final, in which it went out to Panathinaikos on away goals after a 4–4 aggregate. In 1979 it played its first European final, the UEFA Cup final, losing 2–1 on aggregate to Borussia Mönchengladbach.
The absolute peak came in 1991. On the way to the final, coach Ljupko Petrović's side eliminated Bayern Munich in the semi-final, winning 2–1 in Munich and drawing 2–2 in Belgrade. On 29 May 1991, at the Stadio San Nicola in Bari, a generation featuring Dejan Savićević, Robert Prosinečki, Siniša Mihajlović, Darko Pančev and Miodrag Belodedić met Olympique de Marseille. The match finished 0–0 after extra time. In the shoot-out, the first Marseille penalty, taken by Manuel Amoros, was saved by Red Star captain and goalkeeper Stevan Stojanović, after which every penalty was converted and Red Star won 5–3, with Pančev scoring the decisive kick. Crvena zvezda became the first Yugoslav club to win the European Cup, and only the second from Eastern Europe after Steaua Bucharest in 1986. In December 1991 it added the Intercontinental Cup in Tokyo, beating Chile's Colo-Colo 3–0, which makes it the only Yugoslav club ever to be crowned world champion.
Domestically, Red Star remains the dominant force. The 2025/26 season brought its ninth consecutive Serbian title and, by the club's own count, its 37th national championship overall, clinched in April 2026 with a 3–0 win over Partizan in the Eternal Derby. The club also won the Serbian Cup that season, the 30th in its history, completing a sixth consecutive league and cup double. Between April 2017 and December 2025 it went 159 league matches at home without defeat, a streak that ended only with a 1–0 loss to Vojvodina on 7 December 2025.
The club's atmosphere is shaped by its supporters' group, the Delije, and by the Eternal Derby against Partizan, one of the most intense fixtures in European football. For Red Star, the 1991 triumph in Bari remains the reference point against which every later season is measured.