Planet
The smallest known planet is PSR B1257+12A, one of the first extrasolar planets discovered, which was found in 1992 in orbit around a pulsar. Its mass is roughly half that of the planet Mercury. The smallest known planet orbiting a main-sequence star other than the Sun is Kepler-37b, with a mass (and radius) slightly higher than that of the Moon.
Island
Greenland is the world's largest island, with an area of over 2.1 million km, while Australia, the world's smallest continent, has an area of 7.6 million km, but there is no standard of size that distinguishes islands from continents, or from islets.