Modelling the transport of cosmic rays (CRs) in the heliosphere represents a global challenge in the field of heliophysics, in that such a study, if it were to be performed from first principles, requires the careful modelling of both large scale heliospheric plasma quantities (such as the global structure of the heliosphere, or the heliospheric magnetic field) and small scale plasma quantities (such as various turbulence-related quantities). Here, recent advances in our understanding of the transport of galactic cosmic rays are reviewed, with an emphasis on new developments pertaining to their transport coefficients, with a special emphasis on novel theoretical and numerical simulation results, as well as the CR transport studies that employ them. Furthermore, brief reviews are given of recent progress in CR focused transport modelling, as well as the modelling of non-diffusive CR transport.

We review recent observations and modeling developments on the subject of galactic cosmic rays through the heliosphere and in the Very Local Interstellar Medium, emphasizing knowledge that has accumulated over the past decade. We begin by highlighting key measurements of cosmic-ray spectra by Voyager, PAMELA, and AMS and discuss advances in global models of solar modulation. Next, we survey recent works related to large-scale, long-term spatial and temporal variations of cosmic rays in different regimes of the solar wind. Then we highlight new discoveries from beyond the heliopause and link these to the short-term evolution of transients caused by solar activity. Lastly, we visit new results that yield interesting insights from a broader astrophysical perspective.

The regions of interaction between solar wind streams of different speed, known as corotating interaction regions, form an almost constantly existing structure of the inner heliosphere. Using observational data on the main characteristics of the heliosphere, important for GCR modulation, and the results of 3D MHD modeling of corotating interaction regions, and Monte Carlo simulation of recurrent GCR variations, we analyze the importance of the corotating interaction regions for longitude-averaged characteristics of the heliosphere and GCR propagation, and possible ways for simulating long-term GCR intensity variations with respect to the corotating interaction regions.