This is a summary of the reports presented to the 22nd IAEA Fusion Energy Conference, Magnetic confinement theory and modelling section (Geneva, October 2008). Many of the papers are devoted to the investigation of transport processes, in particular to the toroidal momentum transport. Simulation by gyrokinetic codes has been improved in many countries, and the number of available codes reaches several tens. Numerical developments tend to follow the same trend as improvements in the computation power. The timescale for plasma simulations is now comparable to the ion–ion collision time. To improve the predictions for ITER, the near future advances are the combination of gyrokinetic and fluid codes. Reports on stellarators confirm that in these devices the neoclassical transport dominates, but the influence of turbulent transport can play a role in improved confinement regimes and in the resilience of pressure profiles. The resonant magnetic perturbations, mitigating the ELMs, could brake the plasma rotation, increasing the danger of disruption. The problems on the scrape-off layer and the divertor attract a large number of theoretical works that could lead to a better understanding of periphery plasma processes. ITER and reactor studies have been presented, and calculations confirm that ITER can achieve Q = 10 or larger. It has also been shown that the alpha-particle diffusion due to drift driven ITG turbulence will be relatively small in ITER, uncertainty remains in the magnitude of alpha-particle diffusion due to Alfvén waves.