In the process of modeling complex systems based on data, a large amount of uncertain knowledge prevails. Generally, the randomness of the objective system and the ambiguity of human cognition constitute the basic connotation of uncertainty. To formally describe the uncertain information and promote human understanding of the actual system, various uncertain theories have been greatly developed in recent years. Therefore, the source, classification and characteristics of uncertainty are firstly given. Then, from the randomness, fuzziness and mixed uncertainty, this paper systematically summarizes the researches of Bayesian inference, fuzzy inference, rough set, grey theory and evidence theory on the expression and inference of uncertain information. The typical applications of the above theories in engineering practice are discussed from three aspects: reliability engineering, information fusion and decision support. Finally, based on a brief summary of the existing work, three major challenges faced by uncertainty theory in the future development are proposed, and potential solutions are given to provide some reference for researchers in this field.