6 wins & 24 nominations
- 1977 Nominee Brit
- British Group
- 1991 Nominee ACE
- Performance in a Music Special
- 2018 Winner Grammy
- Best Traditional Blues Album
For the album "Blue & Lonesome"Shared with: Charlie Watts - 2014 Winner Grammy
- Best Historical Album
For "Charlie Is My Darling - Ireland 1965" artist: The Rolling Stones
- 2009 Nominee SLFCA Award
- Best Music
Nomination for Hendrix was posthumous.Shared with: The Kinks · The Turtles · Jimi Hendrix · Duffy · Procol Harum · The Box Tops · The Beach Boys · Dusty Springfield · The Seekers · The Who · Smokey Robinson · Chris Andrews · Skeeter Davis · The Troggs · Jeff Beck · The Hollies · David Bowie · The Tremeloes · Lorraine Ellison
- 2025 Nominee Gold Derby Music Award
- Best Rock/Alternative Album
For "Hackney Diamonds"Shared with: Don Was · Andrew Watt
- 1995 Nominee MTV Europe Music Award
- Best Live Act
- 2022 Nominee American Music Award
- Favorite Touring Artist
- 1981 Nominee American Music Award
- Favorite Pop/Rock Band/Duo/Group
- 1966 Nominee NME Award
- World Vocal Group
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