The pattern of insolation on an extrasolar planet has profound implications for its climate and habitability. A planet’s insolation regime depends on its orbital eccentricity, the obliquity of its spin axis, its rotation rate, and its longitude of vernal equinox. For example, although a planet receives the same time-averaged insolation at both poles, the peak insolation at its poles can differ by a factor up to 27, depending on its eccentricity and equinox. This is of particular interest for planets with polar icecaps (or lakes and seas), like Mercury, Earth, and Mars (or Titan). The nearly 600 exoplanets now with known eccentricities span a wide range of eccentricity from essentially zero up to near unity; but their obliquities are still unknown, and also may range widely.Including both non-zero eccentricity and obliquity together vastly broadens the variety of global insolation patterns on extrasolar planets. This applies especially to planets in synchronous rotation, or in other spin-orbit resonances (like Mercury), which can exhibit quite complicated and unusual insolation patterns. For example, regions of eternal daylight and endless night occur only on synchronous exoplanets, whose rotation periods equal their orbital periods; but the peak and time-averaged insolation can vary by factors of at least 32 and 88, respectively, over a planet with a rotation period of half its orbital period, an eccentricity of 0.20, and an obliquity of 60°. Patterns of both mean and peak insolation display various symmetries with respect to latitude and longitude on the planet’s surface. Most of these are relatively simple and easily understood; for example, a resonant planet whose orbital period is half of an odd multiple of its rotation period (as in Mercury’s 3/2 resonance) experiences identical insolation patterns at longitudes 180° apart. However, such half-odd resonances also exhibit a totally unexpected symmetry of the time-averaged insolation with respect to the planet’s equator, not shared by the peak insolation, or by any whole-number resonances. This emergent symmetry can be understood by Fourier analysis of the time-varying insolation.