The behaviour of bubbles in cavitation and boiling processes is determined by the thermodynamic parameters of the two-phase medium and the intensity of heat and mass transfer, which affect the final dynamic effects. In this review, we analyse the influences of these factors on bubble behaviour, as described in existing mathematical models. In particular, we analyse the physical processes that govern bubble behaviour, the influence of mass transfer, vapor and liquid temperature, vapour, and liquid pressure on the inertial and dynamic stages of development. In conclusion, we summarize the problems associated with modelling, the accuracy of numerical predictions, and propose directions for further research.