Visualization has significantly changed the way humans analyze large amounts of multi-dimensional data. However, current visualization techniques can give only little or no guarantees regarding the confidence in the displayed information. Since this information is always affected by uncertainties in the data generation and visualization processes, the user can be lead to misclassifications, misinterpretations, and false assumptions.This proposal challenges the status quo in visual data analysis with innovative ideas for next-generation technology that provides uncertainty visualization as a core methodology. We will develop a visual language for the communication of the variability of features due to uncertainties in the data generation and visualization processes. Our research aims at modeling the uncertainty stochastically and deriving probability distributions for the occurrence of features. Especially in 3D, finding meaningful visualizations of the effect of uncertainty is extremely demanding and requires going far beyond existing approaches.Besides radically changing the way visual data exploration is performed, our research has the potential to strongly influence the way scientific measurements and computer simulations are carried out. The precise knowledge of uncertainties enables to discover quantitatively the data generation process, and it can, therefore, be used to quantify the sensitivity of a process and the generated results to the choice of parameterization over the input parameters. Hence, it is our second vision to position uncertainty visualization as a future technology for guiding research towards the most reliable data generation process within a given uncertainty tolerance.