We present a review of our work on data acquired by GEOSTAR-class (GEophysical and Oceanographic STation for Abyssal Research) observatories deployed at three EMSO (European Multidisciplinary Seafloor and water-column Observatory; http://www.emso-eu.org) sites in southern European waters where strong geo-hazards are present: the Western Iberian Margin, the Western Ionian Sea, the Marmara Sea, and the Marsili basin in the Tyrrhenian Sea. A procedure for multiparameter data quality control is described. Then we explain why the seafloor is an interesting observation point for geophysical parameters and how it differs from land sites. We consider four interesting geophysical phenomena found at the EMSO sites that are related to geo-hazard. In the first case, we show how unknown seismicity and landslides in the Western Ionian Sea were identified and roughly localised through a single-sensor analysis based on the seismometer. In the second case, we concentrate on the problem of near-coast tsunami generation and describe a Tsunami Early Warning Detection (TEWD) system, tested in the Western Iberian Margin and currently operating in real time at the Western Ionian site. In the third case, we consider two large volcanoes in the central Mediterranean area, Mt. Etna and the Marsili seamount. Signals from the seismometer and gravimeter recorded at the seafloor at 2100 m b.s.l. show various phases of Mt. Etna's 2002–2003 eruption. For the less-known Marsili we illustrate how several indicators coming from different sensors point to hydrothermal activity. A vector magnetometer at the two volcanic sites helps identify the magnetic lithospheric depth. In the fourth and final case, we present a multiparameter analysis which was focused on finding possible correlations between methane seepage and seismic energy release in the Gulf of Izmit (Marmara Sea).