Greig played under 19s football for Hawthorn in the Victorian Football League (VFL) during the 1980s, captaining the team and winning its best and fairest award in 1985; despite this, Hawthorn did not wish to retain him, and it released him at the end of 1985.
He polled ten J. J. Liston Trophy votes in only nine games, and Camberwell coach Gary Brice described Grieg's performances as the sole shining light in a winless season which turned out to be the club's last in the VFA.
On debut in Round 21, 1991, at nearly 23 years of age, he compiled a league record 39 disposals (23 kicks, 16 handballs) against Carlton, the VFL/AFL record for most ever disposals on debut.
[2] A strongly built midfielder, he didn't progress as expected, nevertheless managed some fine games with the St Kilda and was noted for his creative handball.
In August 2001, whilst playing for Scoresby Football Club in the Eastern Football League (Australia), he suffered a broken tibia and fibula and due to the onset of compartment syndrome and infection, had his lower leg amputated.