Volcanic eruptions are amongst the most intense and majestic display of natu- re's power that can dramatically impact the Earth system and our modern societies. The recent 2010 eruption of Eyjafjallajökull demonstrated how eruptions of moderate size can impact modern globalised societies. Most of the European airspace was closed for a week and the air traffic over the North Atlantic was interrupted. 313 airports were closed, 104,000 flights cancelled, 10 million passengers stranded, causing a total loss of income of $1.7 billion to airlines and $317 million to airports, for a total economic loss of $5 billion. In order to predict and mitigate the consequences of future volcanic eruptions, risk assessments are required to combine natural hazards, i.e. the physical study of natural phenomena, and the response of exposed elements. The aim of this thesis is therefore to explore new ways to i) better constrain the uncertainty associated with the geological record, ii) better account for uncertainties when modelling the occurrence of future hazards, iii) describing as- pects of vulnerability at different scales and iv) provide operational tools to increase the preparedness for future eruptions.