Southern Italy is one of the most tsunamigenic areas in the Mediterranean basin, having experienced during centuries a large number of tsunamis, some of which very destructive. In particular, the most exposed zone here is the Messina Straits separating the coasts of Calabria and Sicily that was the theatre of the strongest Italian events. In 1783-1785 Calabria was shaken by the most violent and persistent seismic crisis occurred in the last 2000 years. Five very strong earthquakes, followed by tsunamis, occurred in a short interval of time (February-March 1783), causing destruction and a lot of victims in a vast region embracing the whole southern Calabria and the Messina area, Sicily. In this study we re-examined these events by taking into account all available historical sources. In particular, we focussed on the 5 and 6 February 1783 tsunamis, that were the most destructive. As regards the 5 February event, we found that it was underestimated and erroneously considered a minor event. On the contrary, the analysis of the sources revealed that in some localities the tsunami effects were quite strong. The 6 February tsunami, the strongest one of the sequence, was due to a huge earthquake-induced rockfall and killed more than 1500 people in the Calabrian village of Scilla. For this event the inundated area and the runup values distribution were estimated. Further, the analysis of the historical sources allowed us to find three new tsunamis that passed previously unnoticed and that occurred during this seismic period. The first one occurred a few hours before the large earthquake of 5 February 1783. The second was generated by a rockfall on 24 March 1783. Finally, the third occurred on 9 January 1784, probably due to a submarine earthquake.