Abstract: Radiation doses at aircraft altitudes are mainly due to energetic particles from the universe that create secondaries in the Earth's atmosphere. The primary cosmic rays at energies of about 1 to several tens of GeV come permanently from our galaxy, presumably from acceleration regions in supernovae or their remnants. The Sun has a twofold influence: on the one hand its variable magnetic field modulates the penetration of galactic cosmic rays in the heliosphere on time scales ranging from a few days, due to coronal mass ejections, to the solar activity cycle. On the other hand the Sun itself may on occasion accelerate protons and ions to GeV energies and thereby create a supplementary radiation dose at times of high solar activity, when the galactic cosmic ray intensity itself is reduced by the heliospheric magnetic field. This talk will illustrate the French SIEVERT system of aircrew dosimetry, with emphasis on solar energetic particle events. Only very strong and extremely rare solar events appear to make relevant contributions to the radiation doses aboard aircraft. We will illustrate some difficulties with forecasting these events, even on rather short term (some tens of minutes), and relate recent work on the quantitative assessment of extreme solar energetic particle events.