Our knowledge from underground reservoirs is not complete and is limited to some sparse core and log data, seismic data, geological interpretations, etc. This limited knowledge leads to a significant extend of uncertainty that is common in reservoir modeling and characterization. This kind of uncertainty is known as the geological uncertainty since the uncertainty is present in geological parameters, such as permeability, porosity, fluid contacts, reservoir compartmentalization, fault transmissibility, existence, type, and characteristics of aquifer, etc. Accordingly, geological uncertainty can have different scales including the macro- and micro-scale geological uncertainties. This chapter introduces the geological uncertainty, geological uncertainty scales, geological prior information, structural and stratigraphic uncertainties, geological parametrization, use of seismic and petrophysical data in uncertainty quantification, exploring the range of scenarios, geological realizations, and the geostatistical methods to generate geological realizations. The main geostatistical techniques for generating the realizations of the uncertain parameters, including the kriging-based, object-based, and multiple-point geostatistical methods, are introduced, and their applications, advantages and disadvantages are presented.