The current statistical picture of the world is probably the best it has ever been. But it also entails major limitations. In this article we show the limitations by focusing on three key areas: security, economy of development and the environment, and argue that they undermine the performance of global governance, and the possibility of global policy. In particular they do not allow taking the full measure and managing optimally the changes underway at the global level. To overcome this state of affairs, upgrading statistical capabilities is critical. To achieve this objective, the article suggests, among other ideas: adjusting and adapting the conceptualization, collection and implementation of statistical data to a world that is on its way to becoming global; improving the conditions of compilation of statistical data in developing countries; and investing in institution-building and innovation, in developed and developing countries, and in national and international organizations.