He won the inaugural Brownlow Medal in 1924, awarded to the VFL/AFL player adjudged fairest and best during the home-and-away season.

In the 1860s, Greeves' grandmother Julie (née Anderson) was briefly engaged to Tom Wills, the famed cricketer and founder of Australian rules football.

Historian Col Hutchinson noted that "If Tom Wills had married Julie, we wouldn't have had Carji Greeves".

[1] Greeves was given the nickname "Carji" as a baby by a friend of the family, the New South Wales golfer Michael Scott,[2] most likely after a character in A Country Girl, a popular musical play of the day.

[7] Victoria 15.13 (103) defeated Western Australia 14.11 (95), at North Hobart Oval, 9 August 1924, crowd: 15,687 Victoria 14.26 (110) defeated New South Wales 4.6 (30), at North Hobart Oval, 12 August 1924, crowd: 350