In this paper we demonstrate the potential of the infrared Fourier transform spectrometer IASI in analysing volcanic eruptions, using the September 2007 eruption at Jebel at Tair as an illustrative example. Detailed radiative transfer calculations are presented, simulating IASI-like transmittance spectra for a variety of volcanic plumes. We analyse the sensitivity of IASI to SO2 at different altitudes and demonstrate that IASI is in principle capable of sensing SO2 down to the surface. Using the brightness temperature difference of well chosen SO2 channels as a filter, we are able to track the plume of the Jebel at Tair eruption for 12 days, on a par with state of the art UV sounders. A method is presented for quickly estimating the altitude of a volcanic plume based on the relative intensities of the SO2 absorption lines. Despite recent advances, it is still very challenging to retrieve vertical profiles of SO2 from nadir viewing satellites. Currently the most accurate profiles in nadir are retrieved using backtracking of the plume with atmospheric transport models. Via full inverse retrievals using the optimal estimation method, we show the possibility of extracting medium coarse vertical profiles from IASI data. The retrieval allows us to present an evolution of the total mass of SO2 in the plume for the Jebel at Tair eruption. An analytical relation is derived between brightness temperature differences and concentrations, which fits the experimental data very well. The spectral range of IASI also allows retrieval of volcanic aerosols. In the initial plume of the Jebel at Tair eruption, volcanic aerosols were found in the form of ice particles, for which we derived particle sizes.