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NASA's Kepler Space Telescope has collected high-precision, high-cadence timeseries photometry on 781,590 unique postage-stamp targets across 21 differentfields of view. These observations have already yielded 2,496 scientificpublications by authors from 63 countries. The full data set is now public andavailable from NASA's data archives, enabling continued investigations anddiscoveries of exoplanets, oscillating stars, eclipsing binaries, stellarvariability, star clusters, supernovae, galaxies, asteroids, and much more.  In this white paper, we discuss 21 important data analysis projects which areenabled by the archive data. The aim of this paper is to help new usersunderstand where there may be important scientific gains left to be made inanalyzing Kepler data, and to encourage the continued use of the archives. Withthe TESS mission about to start releasing data, the studies will inform newexperiments, new surveys, and new analysis techniques. The Kepler mission hasprovided an unprecedented data set with a precision and duration that will notbe rivaled for decades. The studies discussed in this paper show that many ofKepler's contributions still lie ahead of us, owing to the emergence ofcomplementary new data sets like Gaia, novel data analysis methods, andadvances in computing power. Kepler's unique data archive will provide newdiscoveries for years to come, touching upon key aspects of each of NASA'sthree big astrophysics questions; How does the universe work? How did we gethere? Are we alone?

Kepler's Discoveries Will Continue: 21 Important Scientific Opportunities with Kepler & K2 Archive Data