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The rotation of a star and the revolutions of its planets are not necessarily aligned. This article reviews the measurement techniques, key findings, and theoretical interpretations related to the obliquities (spin-orbit angles) of planet-hosting stars. The best measurements are for stars with short-period giant planets, which have been found on prograde, polar, and retrograde orbits. It seems likely that dynamical processes such as planet-planet scattering and secular perturbations are responsible for tilting the orbits of close-in giant planets, just as those processes are implicated in exciting orbital eccentricities. The observed dependence of the obliquity on orbital separation, planet mass, and stellar structure suggests that in some cases, tidal dissipation damps a star's obliquity within its main-sequence lifetime. The situation is not as clear for stars with smaller or wider-orbiting planets. Although the earliest measurements of such systems tended to find low obliquities, some glaring exceptions are now known in which the star's rotation is misaligned with respect to the coplanar orbits of multiple planets. In addition, statistical analyses based on projected rotation velocities and photometric variability have found a broad range of obliquities for F-type stars hosting compact multiple-planet systems. The results suggest it is unsafe to assume that stars and their protoplanetary disks are aligned. Primordial misalignments might be produced by neighboring stars or more complex events that occur during the epoch of planet formation.