The development of large-scale fireballs is a typical result of explosions associated with accidental fuel releases in the oil and process industries. The two major mechanisms that lead to fireball formation are vapour cloud explosions and boiling liquid expanding vapour explosions (BLEVEs). An ability to model fireballs is extremely important from the point of view of safety and risk analysis. The present paper provides a state-of-the-art review of the computational techniques available for the mathematical modelling of fireballs. The emphasis is placed on computational fluid dynamics (CFD) modelling, based on Reynolds-averaged Navier-Stokes (RANS) equations for reactive flow. The results of calculations and estimations of fireball hazards are compared with available experimental data. New results are presented for problems that are usually given less attention in fireball studies. These concern estimations of air entrainment rates into fireballs and potential strategies for fireball suppression.