Geoinformatics documentations, e.g., relational databases, generally consist of single-valued input data, that is, of real numbers. The uncertainties related to these data are not expressed. As a consequence, the results of data set evaluations can be considered as statements, but their reliability is not quantified. The introduction of uncertainties quantification into geoinformatics would be highly useful. One of the main difficulties is that the related concepts are not clarified and properly defined; in some cases they are even contradictory. The aim of this paper is to clarify the basic concepts related to geological uncertainties and to call attention to some new mathematical methods, suitable to quantify the uncertainties at the database level and to express the reliability of evaluation results. In the first part of the paper, the mathematical and the suggested geological classifications of uncertainties are presented. The role of “frequentist” and “Bayesian” information and probabilities are discussed. Limitations of probability theory for uncertainty analysis are shortly outlined. In the second part of the paper, the “uncertainty-oriented” mathematical methods are outlined, such as interval analysis, fuzzy set theory, possibility theory, probability bounds theory, and various hybrid methods. The authors describe their experience in the geological application of some of these methods. Test calculations, preformed by the authors, are listed before presenting some concluding remarks.