| Scottish League Champions: | 1931/32 |
| Runners-Up: | 1926/27, 1929/30, 1932/33, 1933/34, 1994/95, 2012/13, 2013/14 |
| Scottish Cup Winners: | 1952, 1991 |
| Runners-Up: | 1931, 1933, 1939, 1951, 2011, 2018 |
| Scottish League Cup Winners: | 1950 |
| Runners-Up: | 1954, 2005, 2017 |
| Scottish 1st Division Champions: | 1981/82, 1984/85 |
| Scottish 2nd Division Champions: | 1953/54, 1968/69 |
| Runners Up: | 1894/95, 1902/03 |
| Scottish Summer Cup Winners: | 1944, 1965 |
| Scottish Second XI Cup Winners: | 1949, 1951, 1957 |
| Scottish Reserve League Cup Winners: | 1988 |
| Scottish Southern League Cup Winners: | 1945 |
| Scottish Youth Cup: | 2016 |
| Milk Cup: | 1983 |
| UEFA Participation | |
| UEFA Champions League: | 2012/13 |
| European Cup Winners’ Cup: | 1991/92 |
| UEFA Cup: | 1994/95, 1995/96, 2008/09 |
| Europa League: | 2009/10, 2010/11, 2012/13, 2013/14, 2014/15 |