Automatic cleaning of MultiBeam EchoSounder (MBES) bathymetric datasets is a critical issue in data processing especially with the objective of nautical charting. A number of approaches have already been investigated in order to provide solution in views of operationally reaching this still challenging problem. This paper aims at providing a comprehensive and structured overview of existing contributions in the literature. For this purpose, a taxonomy is proposed to categorize the whole set of automatic and semi-automatic methods addressing MBES data cleaning. The non-supervised algorithms that compose the majority of the methods developed in the hydrographic field, are mainly described according to both the features of the bathymetric data and the type of outliers to detect. Based on this detailed review, past and future developments are discussed in light of both implementation and test on datasets and metrics used for performances assessment.