This review summarizes the biological and ecological factors of hexaploid wheat (Triticum aestivum L.) that contribute to trait movement including the ability to volunteer, germination and establishment characteristics, breeding system, pollen movement, and hybridization potential. Although wheat has a short-lived seedbank with a wide range of temperature and moisture requirements for germination and no evidence of secondary dormancy, volunteer wheat populations are increasing in relative abundance and some level of seed persistence in the soil has been observed. Hexaploid wheat is predominantly self-pollinating with cleistogamous flowers and pollen viability under optimal conditions of only 0.5 h, yet observations indicate that pollen-mediated gene flow can and will occur at distances up to 3 km and is highly dependent on prevailing wind patterns. Hybridization with wild relatives such as A. cylindrica Host., Secale cereale  L., and Triticum turgidum L. is a serious concern in regions where these species grow in field margins and unmanaged lands, regardless of which genome the transgene is located on. More research is needed to determine the long-term population dynamics of volunteer wheat populations before conclusions can be drawn with regard to their role in trait movement. Seed movement has the potential to create adventitious presence (AP) on a larger scale than pollen, and studies tracing the movement of wheat seed in the grain handling system are needed. Finally, the development of mechanistic models that predict landscape-level trait movement are required to identify transgene escape routes and critical points for gene containment in various cropping systems.