[3] Greive joined the Australian Army after leaving high school and underwent training at the Royal Military College Duntroon in Canberra.

[10] In late 2013, Greive purchased the English language gift-book rights to Bertrand Russell's seminal essay, 'In Praise of Idleness'.

[11] In 1996 Greive became a creative consultant and writer for Godfrey Bigot's weekly political sketches on Channel 7's Today Tonight, and went on to pursue a similar role in 1997 with MTV Australia.

[14][15][16] In 2007 he wrote, produced and hosted The World According to Bradley Trevor Greive on Tasmania's community radio station Star FM .

[20] Over December 2009 and January 2010, Greive presented ABC Radio National Evenings (hosted by Christopher Lawrence) with his 'E-Mail From America'[21] – a weekly series of eclectic and humorous reports from Florida, USA.

[30][31] Shortly after retiring from his career as a paratrooper in 1993, Greive worked in several entry-level positions in the advertising, modelling and service industries which he has described as "creatively enlightening".

[2][35] In late 2013 Greive signed with the United Talent Agency, who now represent him for film, stage, radio, lectures and television work.

In 2002 Greive teamed up with famed Japanese wildlife photographer, Mitsuaki Iwago, to produce a book on biodiversity entitled Priceless – The Vanishing Beauty of a Fragile Planet.

The book has inspired numerous people to take positive action in regards to wildlife conservation, including British filmmaker, Steve Piper, who went on to make an acclaimed documentary about critically endangered Scottish Wildcats.

[51] Despite his many media appearances, Greive is known to be a very private person: a "self-described cave bear by nature, who equates publicity to 'being stoned to death with toffee apples'".

[1][5] Greive's hobbies and interest include sky-diving, desert racing, scuba diving, wildlife, adventure travel, art, cooking, science, and reading.

Greive has been quoted as saying his favourite fictional character is "the lace-making, latently heroic Beaver from Lewis Carroll's Hunting of the Snark".