Cosmic rays in the heliosphere: progress in the modelling during the past 10 years

During the past 10 years the modelling of the transport of cosmic rays in the heliosphere has evolved from pure test particle simulations to more consistent treatments. Improvements comprise an explicit and simultaneous treatment of the plasma turbulence with which the cosmic ray particles interact, the consideration of a non-spherical modulation volume resembling the large-scale heliosphere, and the dynamics of the heliosphere on various time-scales. At the same time, the progress made regarding the theory of the transport of energetic charged particles in electromagnetic turbulence is reflected in the cosmic ray modelling by the use of a fully-anisotropic diffusion tensor as well as a rigorous approach to the description of perpendicular diffusion both of which are significant improvements of earlier ad-hoc assumptions. The state-of-the-art of the modelling is reviewed.