Kepler was launched on 7 March 2009. The primary objective of the mission was to survey a single area of the sky (in the direction of Cygnus) to determine the frequency of Earth-sized planets in the habitable zone of their parent stars. A secondary objective was to study the interior physics of stars via asteroseismology. Of course, the high photometric precision and nearly continuous observing window has enabled science across a wide range of astrophysics. The spacecraft has a wide, optical bandpass designed to maximize the flux throughput from solar-like stars. On 11 May 2013, the spacecraft lost operation of a second reaction wheel, effectively ending the original mission. A second survey, called "K2", began in March of 2014 using the two remaining reaction wheels to balance with the solar wind. The K2 mission points at many different fields in the sky (called "Campaigns") along the ecliptic plane. Although it has worse precision that the original mission, it's still very good, and as a bonus, the trick of balancing the spacecraft with the solar wind forces the spacecraft to observe many different fields that include lots of interesting targets that were not observed with the original mission. The K2 mission ended on 30 October 2018 when the spacecraft ran out of fuel. The final commands ("goodnight commands") were sent to the spacecraft on 15 Nov. 2018.

Kepler "Objects of Interest" (or KOIs for short) are exoplanet signals found by the Kepler team that pass a variety of sanity checks, performed by both human and artificial means. This doesn't mean the KOIs represent a complete list of exoplanet candidates, and it doesn't mean they are all real planets, but they represent the best set of exoplanet candidates detected by the mission pipeline. And there are a lot of them: 4,034 planet candidates in the final version of the catalog that the Kepler team put together. But even with a lot of calibration and care, there will always be "false positive" signals. There are a number of sources, but the most common cause aside from instrumental noise, are eclipsing binaries of one form or another. An eclipsing binary, where two stars cross in front of each other to our line-of-sight, can look a lot like a giant planet, especially if there is extra light from some other star(s) blending in with it.

Fortunately, there are several ways to check for these. One of the most direct ways is to obtain a series of spectra of the purpoted planet host star: either you'll see the star wobble a lot (if another star is causing the signal you thought was due to a planet) or not at all (if the star you were looking at is actually just minding its business, and the actual signal was caused by some other pair of stars in the background). The figure above shows different scenarios and how often you can detect them by placing a fiber that covers the area on sky denoted by the circles, and leads into a spectrograph. If you have really good precision, you can see the star wobble due to a planetary mass companion: in which case you not only validated the planet, you measured its mass! I'm part of a group that does exactly this, but in bulk, using the multi-object, near-infrared APOGEE spectrograph. Sometimes we identify KOIs that are not caused by planets, sometimes we find out what we thought was a planet is actually a brown dwarf, and sometimes we are able to validate that indeed the signal is caused by a planet!

Kepler's exquisite photometry is not only good for finding planets that cross in front of their host star: it's enabled a wide range of stellar astrophysics, including the study of stars that cross in front of each other relative to our line-of-sight. By measuring with very high precision how the brightness of the two stars change as they orbit around and in front of one another, we can tell a lot about the stars themselves. In particular, we can derive the relative sizes of the stars with great precision, which can give us the stars' radii. In most cases, however, we aren't able to determine their masses. But, if you monitor eclipsing binaries with spectrographs, you can measure the wobble each star causes on the other, and in this way measure their masses. If you can measure this wobble very carefully, you can thus measure both very precise masses and radii for the stars in the system, and enable comparision of these values with model predictions. In particular, models often don't agree with derived masses and radii for low mass dwarfs (K and M dwarfs), and the exact cause is still under investigation. Below you can see the calibrated Kepler "lightcurve" (brightness of the system as a function of time), and the two "dips" caused by the two stars crossing in front of each other. The big dips happen when the cooler and smaller of the two stars blocks some of the light from the larger, hotter star. The smaller dips happen when the cooler star goes behind the warmer, larger star.