In this paper, both the current knowledge and hypotheses about the modulation and the transport of cosmic rays in the heliosphere are reviewed. The transport theory aims at an understanding of all processes determining the propagation of cosmic rays in the solar wind plasma. Keys to fulfill this task are to measure the cosmic ray distribution in the three-dimensional heliosphere and to model the cosmic ray transport in the solar wind. The main unknowns in the models are the diffusion tensor, the importance of drifts and the local interstellar spectra. Drift effects depend on the charge sign of the particle and the polarity of the heliospheric magnetic field. Therefore it is important to analyze particles with opposite charge sign simultaneously. On the modelling side it is vital to include all modulation processes in transport models. Recent modelling has advanced to a self-consistent treatment of the dynamic heliosphere and the cosmic ray transport. This opens the unique opportunity to study long term modulation on time scales of centuries.

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