Maritime mobility monitoring can be achieved through remote sensing and self-reporting systems, which produce large datasets enabling the extraction of valuable information on global shipping trends. This extraction can be defined as a data mining task of transforming huge amounts of geospatial data, into a descriptive and compact data model, that can then be used for identifying the underlying relationships or patterns. In this work, we present a brief overview of mobility data mining as applied to the maritime use case. We highlight its unique aspects, identify six major data mining tasks, discuss indicative approaches found in literature, and address some challenges for future work.