This paper gives an overview of the research that has been conducted to get a better understanding of the navigation in ports and waterways with fluid mud layers. In particular, the up-to-date review of reported full scale experiments that involve real vessels is provided. To study physical processes, the full scale experiments are accompanied by scaled experiments and numerical modelling. This combination provides a valuable insight into ship behavior with respect to different navigation conditions and physical properties of fluid mud. Another aspect of this paper are the surveying methods that can localize the fluid mud layers and potentially provide information about the strength of these layers. Some of these methods were tested on fluid mud produced by water injection dredging in the Port of Rotterdam. It was concluded that the new rheology-based method show a potential for understanding of strength development in fluid mud layers. Finally, some open research questions with respect to the applicability of the navigation through fluid mud are discussed.