We are in the midst of a major paradigm shift in how we manage radio spectrum. This paradigm shift is necessitated by the growth of wireless services of all types and the demand pressure imposed on limited spectrum resources under legacy management regimes. The shift is feasible because of advances in radio and networking technologies that make it possible to share spectrum dynamically in all possible dimensions---i.e., across frequencies, time, location, users, uses, and networks. Realizing the full potential of this shift to Dynamic Spectrum Sharing will require the co-evolution of wireless technologies, markets, and regulatory policies; a process which is occurring on a global scale. This paper provides a current overview of major technological and regulatory reforms that are leading the way toward a global paradigm shift to more flexible, dynamic, market-based ways to manage and share radio spectrum resources. We focus on current efforts to implement database-driven approaches for managing the shared co-existence of users with heterogeneous access and interference protection rights, and discuss open research challenges.