We are working to understand how stars of different mass and composition evolve, and how stellar evolution directly influences the location of the habitable zone (HZ) around a star. It is now estimated that more than 20% of all Sun-like stars and 50% of M-dwarfs may host a planet in the HZ, the latter indicated by recent results from NASA’s Kepler mission. We have created a large catalog of stellar evolution models for FGKM-type stars with variable compositions, including the time dependent evolution of HZ boundaries. We want to determine what kind of star could host a planet that would remain “continuously habitable” for at least 2 billion years. This is roughly the time it took for life on Earth to change the atmosphere such that it would be detectable with the kind of space missions recommended in the most recent Decadal Review.