Laplace argued, correctly, that the small inclinations of planetary orbits implied that the solar system formed from a flat disk. The
observational and theoretical evidence on whether extrasolar planetary systems are flat, however, is still ambiguous. I will discuss
constraints on flatness from the Kepler spacecraft and other sources; measurements of the Rossiter-McLaughlin effect in transiting planets; Lidov-Kozai oscillations; and competing migration mechanisms for the formation of giant planets at small orbital radii.