Though Australia is larger than Greenland, Greenland is considered the world's largest island. Australia is considered a continent, so it's technically not an island, geographically-speaking. Australia is the smallest continent in the world, but if it were to be considered an island, other landmasses like Antarctica would also be considered in the ranking.
Greenland has an area of 822,706 square miles, but fewer than 100,000 people live there, as of 2015. Though it is part of Danish territory, Greenland is geographically part of North America. The Pacific island of New Guinea is the next largest island in the world. It has an area of 303,381 square miles.