The increasing use of data in various parts of the economic and social systems is creating a new form of monopoly: data monopolies. We illustrate that the companies using these strategies, Datalists, are challenging the existing definitions used within Monopoly Capital Theory (MCT). Datalists are pursuing a different type of monopoly control than traditional multinational corporations. They are pursuing monopolistic control over data to feed their productive processes, increasingly controlled by algorithms and Artificial Intelligence (AI). These productive processes use information about humans and the creative outputs of humans as the inputs but do not classify those humans as employees, so they are not paid or credited for their labour. This paper provides an overview of this evolution and its impact on monopoly theory. It concludes with an outline for a research agenda for economics in this space.