The main argument of this article is that human living systems are open, dynamic, intentional systems and, therefore, are capable of building ever more complex behaviors through self-organization and self-direction. This principle underlying general human development is also applicable to the development of gifted and talented behaviors. These behaviors are dynamic because persons demonstrating such behaviors are forming dynamic, functional relations with a specific environment, with unique temporal trajectories capable of engendering emergent properties that feed into further development. This Contextual, Emergent, and Dynamic Model provides an alternative to traditional static, reductionistic, trait-based conceptions of giftedness. The article further elaborates on three dynamic facets of the making of gifted potential: selective affinity, maximal grip, and being at the edge of chaos. These facets allow for dealing with the genesis of talents, developing expertise over an extended period, and developing creative potential. (Contains 4 figures, 2 tables, and 1 note.)