Robert grew up in public housing in Chadstone, Victoria, and was golfing by age seven. When he was about 13, he met Steve Bann, a PGA Professional then at Melbourne's Box Hill Golf Club who coached him for 18 years. He turned Professional in 1992 and was soon successful, topping the PGA Tour of Australasia Order of Merit in his first season and again in 1994. Since this time Robert has player predominantly in the US, returning home often to support the PGA Tour of Australasia.
Robert is a patron and spokesperson for Challenge Cancer Support Network. He is an advocate for kids with debilitating illnesses and special needs and donates a lot of time and money to help children. Robert's mother, Sylvia, passed away from lung and kidney cancer in 2009 which strengthened Allenby's desire to raise awareness and money for cancer. During tournaments, Allenby wears pink shirts on Sunday in remembrance of his mother and to show support of women living with cancer.
In 2013 Allenby failed to retain his PGA TOUR card for the first time. He is competing on Tour in 2014 utilising his once only career money exemption.
Allenby in 2016 and 2017 has mainly played on the Web.Com and PGA Tours where he has the one top 10 finish.
Often playing on the Tour of Australasia, Allenby was the 2010 runner up at the Players Championship and is a two time Australian PGA Champion
- 2005: Became the first golfer to win the PGA Tour of Australasia "triple crown" of the Australian Masters, Australian PGA and Australian Open in the same year;
- 2009: Captured the Australian PGA Championship for a fourth time cruising to his second win in as many weeks by four shots from John Senden and Scott Strange;
- Played for the International Team in the Presidents Cup in 1994, 1996, 2000, 2003, 2009 and 2011.
- Represented Australia at the World Cup of Golf in 1993, 1995 and 2009.
- Since 1992 Robert has raised more than US$9million for the Challenge Cancer Support Network.
- In 2014 he received the Charlie Bartlett Award from the Golf Writers Association of America, given to a player whose unselfish contributions have improved society.
- Plays mostly on the PGA and Web.Com Tours