The Australian Republican Movement advocates replacing Australia's Constitutional Monarchy form of government with a Republic. Supporters of the movement are known in Australia as Republicans. Opponents are known as Monarchists.
Australia has been independent of the UK in a practical sense for many decades. However, the Head of State is the Australian Monarch who under the constitution is the same person as the British Monarch, currently Queen Elizabeth II. As the monarch is rarely present in Australia, she is represented there by the Governor General who is appointed by the Australian Prime Minister. The Republican Movement advocates replacing the Monarch and Governor General with an Australian President. There is no general agreement within the movement as to whether the President would be chosen by the government, public, or some other body.
In 1999, the movement was successful in achieving a referendum on the issue, a necessary step for any constitutional change. The Prime Minister of the day, John Howard was a Monarchist which in part explains why the referendum was defeated.
At the time of the referendum the leader of the movement was Malcolm Turnbull, who is now Federal Leader of the Opposition. Current Prime Minister Kevin Rudd is also a Republican. It is therefore possible that the question of an Australian Republic will once again come to the fore.