The interaction between a host star and its orbiting planet can generate both radiative and gravitational effects on planetary climate. While these effects on climate are largely constrained and understood for the Earth, exoplanets fill a much more diverse range of planetary and stellar properties. To identify habitable exoplanets, it is important to understand how the climatic effects of the processes that influence the Earth’s climate might change for different host stars and planetary and orbital characteristics. I will share results from work performed using a hierarchy of models to simulate planets covered by ocean, land and water ice, with incident radiation from stars of different spectral types. Results indicate that ice extent is much greater on a planet orbiting a hotter, brighter star than on a planet orbiting a cooler, redder (M-dwarf) star at an equivalent flux distance, assuming an Earth-like atmospheric concentration of carbon dioxide. I’ll explain the reasons behind this apparent warmer planetary haven around cooler stars, address how the picture changes at the outer edge of the stellar habitable zone, and discuss the implications of our results for planetary climate and habitability. I will also explore a specific case —that of Kepler-62f, a potentially habitable planet in a five-planet system orbiting a K-dwarf star—and discuss its prospects for habitability as a function of atmospheric composition and orbital configuration, based on work performed with both N-body and global climate models. The methods presented can be used to assess the possible climates of potentially habitable planets as they are discovered.