AbstractUncertainty is generally defined as ‘that which is not precisely known’. This definition permits the identification of different kinds of uncertainty arising from different sources and activities, most of which go unnoticed in analysis. In this paper, the evolution of uncertainty through time begins from a historical perspective and concludes with a new perspective based upon making inferences. The evolution of uncertainty, in terms of analytical progress, begins with assessing probabilities and concludes with models and methods for assessing the ‘total uncertainty’ within an application. Both evolutionary tracks are briefly described in the context of physical science and engineering applications; however, nothing presented precludes application to other fields, e.g. economics, social sciences, medicine and business. As we honor his 90th birthday, Zadeh’s fuzzy sets and logic play a prominent role in both evolutions. Uncertainty assessment involves how to identify, classify, characterize, quantify, and combine uncertainties within an application, with the expressed goal of understanding how to manage uncertainties. Managing uncertainties is important, because uncertainties directly affect decision and policy making. Assessment and quantification of uncertainties are generally defined and outlined. Mathematical developments are not provided and in some cases are still under or in need of development.