The paper presents the usage of mathematical theory of evidence in maritime and offshore applications. This paper brings together a collection of some research on the Dempster–Shafer theory of belief functions. By bridging fuzzy logic and probabilistic reasoning, the theory of belief functions has become a primary tool for knowledge representation and uncertainty reasoning in expert systems. This paper can serve as the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in maritime and offshore applications, in management, engineering and transport, in marine shipping, coastal management, navigation, surveillance, monitoring and observation. In particular the paper describes uncertainty reasoning approaches to decision making in maritime and offshore applications, possible applications in safety-based assessment, Coastal Management Expert System, mathematical theory of evidence in marine navigation, the optimisation problem of monitoring stations distribution and finally the facility location and location science.