In this paper hydrodynamic and kinetic approaches to model low-pressure capacitively coupled complex radio-frequency discharges are discussed and applied to discharges under micro-gravity. Complex plasmas contain dust grains with a large negative charge and are characterized by a strong coupling between the properties of the plasma and those of the dust grains. After a discussion of the physics and methods involved, examples are presented from modelling of experiments under micro-gravity in the PKE-Nefedov reactor on board the International Space Station. These discharges are simulated with a 2D cylindrically symmetric hydrodynamic model. Kinetic effects are studied with a 1D particle-in-cell plus Monte Carlo model in which capture and scattering by dust grains is included. Since experiments are often performed at low pressures, the electron energy distribution function is no longer determined by the local plasma properties. This has consequences for the charging of the dust. Results of simulations with this model are compared with the hydrodynamic results. In addition, we address the behaviour of the dust charge in decaying plasmas.