Solar system objects interact differently with the solar radiation and wind plasma, or with magnetospheric plasmas in the case of planetary moons, depending upon their size, upon their own neutral and plasma environment, and upon the presence or absence of an intrinsic magnetic field. This session aims at reviewing the present state of the art in the numerical modelling of these interactions, both from a global scale encompassing the whole environment of the object or from a microscopic scale in order to model specific processes involved in these interactions. Presentations of recent achievements as well as assessments of present and future challenges are welcome.