Planet Nine (or Planet 9) is a theoretical additional planet beyond Neptune, under consideration because of solar system orbit characteristics. In the last decade, a theory has grown from studying the orbits of many minor planets beyond Neptune (i.e., KB objects) and reverse-engineering how the orbits could come to be as they are. Some earlier planets were discovered through observation of orbits of planets, but the current work is based not upon a feature of an individual orbit (and where some unknown planet might have to be to draw it into that position), but of orbits of whole populations of objects and how they came to be that way. Simulations of long-term orbit histories are carried out to explore what could create the current situation. Objects of high interest are six extreme trans-Neptunian objects possessing orbits unaffected by Neptune, thus stable enough to have remained as is for billions of years if not influenced by some as-yet-undiscovered planet. Also of interest are observed TNOs with very high orbital inclinations: irrespective of whether their orbits are stable, there must be some mechanism (such as a planet) that gave them that inclination.
The most widely accepted Planet 9 theory as of 2019 is a planet with a high orbital inclination (15° to 25°), a substantial eccentricity (0.2 to 0.5), in an orbit with semi-major axis 400-800 AU, an orbital period on the order of 10,000 years, and a mass of 5 to 10 Earth masses. Studies have claimed a gas giant at that distance would have been found already by surveys, suggesting a Planet 9 has to be rock or ice.
In the past, there have been other Planet 9 theories. Such a theory led to Pluto's discovery, and it was considered the "found" planet 9 for a while (just as Ceres and other early-found asteroids were considered planets for some time after their early 1800s discovery). Theories were then alive about an additional (10th) planet. Recently, along with the current theories of a 9th planet, there have also been more speculative theories of yet another planet, aka Planet 10: one recent theory suggesting a Mars-mass planet at 62 AU, with an orbital inclination of about 7°.