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.
Sub-Earth
The "Kepler" space telescope opened the realm of sub-Earths by its discovery of them. On January 10, 2012, Kepler discovered the first three sub-Earths around an ordinary star, Kepler-42. As of June 2014, Kepler has 45 confirmed planets that are smaller than Earth, with 17 of them being smaller than 0.8 R. In addition, there are over 310 planet candidates with an estimated radius of <1R, with 135 of them being smaller than 0.8 R.