Solar tracking in the common sunflower, Helianthus annuus, is a dramatic example of a diurnal rhythm in plants. During the day, the shoot apex continuously reorients, following the sun’s relative position so that the developing heads track from east to west. At night, the reverse happens, and the heads return and face east in anticipation of dawn. This daily cycle dampens and eventually stops at anthesis, after which the sunflower head maintains an easterly orientation. Although shoot apical heliotropism has long been the subject of physiological studies in sunflower, the underlying developmental, cellular, and molecular mechanisms that drive the directional growth and curvature of the stem in response to extrinsic and perhaps intrinsic cues are not known. Furthermore, the ecological functions of solar tracking and the easterly orientation of mature heads have been the subject of significant but unresolved speculation. In this review, we discuss the current state of knowledge about this complex, dynamic trait. Candidate mechanisms that may contribute to daytime and nighttime movement are highlighted, including light signaling, hormonal action, and circadian regulation of growth pathways. The merits of the diverse hypotheses advanced to explain the adaptive significance of heliotropism in sunflower are also considered.