Drainage basins in many parts of the world are ungauged or poorly gauged, and in some cases existing measurement networks are declining, The problem is compounded by the impacts of human-induced changes to the land surface and climate, occurring at the local, regional and global scales. Predictions of ungauged or poorly gauged basins under these conditions are highly uncertain. The IAHS Decade on Predictions in Ungauged Basins, or PUB, is a new initiative launched by the International Association of Hydrological Sciences (IAHS), aimed at formulating and implementing appropriate science programmes to engage and energize the scientific community, in a coordinated manner, towards achieving major advances in the capacity to make predictions in ungauged basins. The PUB scientific programme focuses on the estimation of predictive uncertainty, and its subsequent reduction, as its central theme. A general hydrological prediction system contains three components: (a) a model that describes the key processes of interest, (b) a set of parameters that represent those landscape properties that govern critical processes, and (c) appropriate meteorological inputs (where needed) that drive the basin response. Each of these three components of the prediction system, is either not known at all, or at best known imperfectly, due to the inherent multi-scale space-time heterogeneity of the hydrological system, especially in ungauged basins. PUB will therefore include a set of targeted scientific programmes that attempt to make inferences about climatic inputs, parameters and model structures from available but inadequate data and process knowledge, at the basin of interest and/or from other similar basins, with robust measures of the uncertainties involved, and their impacts on predictive uncertainty. Through generation of improved understanding, and methods for the efficient quantification of the underlying multi-scale heterogeneity of the basin and its response, PUB will inexorably lead to new, innovative methods for hydrological predictions in ungauged basins in different parts of the world, combined with significant reductions of predictive uncertainty. In this way, PUB will demonstrate the value of data, as well as provide the information needed to make predictions in ungauged basins, and assist in capacity building in the use of new technologies. This paper presents a summary of the science and implementation plan of PUB, with a call to the hydrological community to participate actively in the realization of these goals.