Burrows has played with world-renowned musicians such as Frank Sinatra, Dizzy Gillespie and Nat King Cole, Oscar Peterson, James Morrison, Tony Bennett, the Sydney Symphony, Stéphane Grappelli and Cleo Laine.
1973 was a watershed year for Burrows in which he received the first gold record won by an Australian jazz musician for his record Just the Beginning; instigated the first jazz studies program in the southern hemisphere at the [Sydney Conservatorium of Music|New South Wales Conservatorium of Music](under the direction of Rex Hobcroft); and was awarded the [Member of the Order of the British Empire] (MBE). In 1979 he was appointed Chair of Jazz Studies at the Conservatorium.
Burrows fronted the nationally televised show The Don Burrows Collection for six years. He has an extensive recording career in his own right with his groups and has performed on many more albums with other artists.
In the 1980s, he associated closely with the then young James Morrison.
In the 2000s, Burrow's public profile has receded somewhat as he performs less than he used to.
In 2005 he toured with a small band including renowned Australian jazz pianist Kevin Hunt. Burrows is using his photographic images with his music in a show called Stop, Look and Listen.
- Member of the Order of the British Empire (MBE), 1973
- Officer of the Order of Australia (AO), 1987
- Life member of the New South Wales Conservatorium of Music, 1988
- Inducted into the ARIA Music Awards Hall of Fame, 1991
- Named one of the Australian Living Treasures, 1989, 1999
- Sir Bernard Heinze Award, for his service to Australia, 2000
- Honorary Doctorate in Music, Sydney University, 2000
- Honorary Doctorate in Music, Edith Cowan University, Perth, 2001
- Ted Albert Award for Outstanding Services to Australian Music, Australasian Performing Right Association (APRA) Awards of 2004
- Honorary Doctorate in Education, Central Queensland University, 2004
- Queen Elizabeth Jubilee medal
- Inducted into the Australian jazz Bell Awards Hall of Fame, 2007
Social matters and interests 
He has had a lifelong hobby of black-and-white photography, beginning in his 20s as an active participant in the Sans Souci and Caringbah camera clubs in Sydney. He sees the creativity of music and photography having significant similarities. He is also an avid fly fisherman.
Burrows has suffered from arthritis since age 38. In a 2008 interview with the Australian Broadcasting Corporation's Andrew Ford, celebrating his 80th birthday, he said "arthritis is not the greatest for playing a musical instrument. But playing a musical instrument is very, very good for arthritis".
This is a partial discography:
- 1966 The Jazz Sound of the Don Burrows Quartet, Columbia Records
- 1969 2000 Weeks (OST), EMI SCXO-7883
- 1971 Just the beginning
- 1972 Live At Montreux, Cherry Pie Records
- 1974 The Don Burrows Quartet at the Sydney Opera House, Cherry Pie
- 1975 The New Don Burrows Quintet
- 1975 Duo, Don Burrows & George Golla, Cherry Pie
- 1975 The Saxophone Artistry Of Don Burrows, Columbia
- 1976 The Tasman Connection, Cherry Pie Records
- 1976 Cool Yule, Cherry Pie
- 1977 Don Burrows and the Brazilian Connection
- 1977 Steph 'n' Us, Stephane Grappelli/Don Burrows & George Golla Duo
- 1977 Don Burrows and the Brazilian Connection, Cherry Pie
- 1978 At The Sydney Opera House, Cherry Pie
- 1979 Bonfa Burrows Brazil, (with Luis Bonfa), Cherry Pie
- 1979 Back in Town, Andrews/Brown/Burrows/Turnbull, 44 records
- 1980 Brazilian Parrot
- 1982 Jazz Brothers - A Retrospective, ABC Music
- 1982 A Night in Tunisia
- 1982 Sara Dane: Music Inspired by the T.V. Series
- 1985 Makin Whoopee, ABC
- 1985 Jazz at the Opera House
- 1986 Flute Salad, Don Burrows & Chris Hinze, ABC
- 1994 Together at last, Julie Anthony & Don Burrows
- 1994 Strings of Swing, Ian Cooper
- 1999 Whenever, Morrison Records
- 2005 Non-stop Flight, Don Burrows & The Mell-o-tones
- Other places other times, Don Burrows & George Golla Duo, Cherry Pie
- Burrows At The Winery, ABC
- Someone who cares, Cherry Pie
- The Babinda Trilogy, Warner Bros. Records
- "'Just the Beginning' on australianscreen online". Retrieved 2011-03-03.
- It's an Honour - Member of the British Empire
- Award-winning jazz performer Kevin Hunt
- It's an Honour - Officer of the Order of Australia
- "2004 Winners - APRA Music Awards". Australasian Performing Right Association (APRA). Retrieved 2 September 2010.
- Jackson, Andra (3 May 2007). "For jazz Hall of Fame, it's plain and simple: is Don, is good". The Age (Melbourne).
- "Don Burrows transcript". Australian Broadcasting Corporation (ABC) The Music Show. 2008-08-09. Retrieved 2008-09-17.
- Listen to a clip from 'Just the Beginning' and read more about it on australianscreen online
- The album 'Just the Beginning' was added to the National Film and Sound Archive's Sounds of Australia Registry in 2010