During solar maximum conditions, the heliosphere is highly structured on all spatial scales. It is the purpose of this paper to summarize our current understanding of these structures from global scales to mesoscale, a fraction of 1 AU. We use theoretical considerations, in situ observations near Earth and the Ulysses spacecraft, and global heliosphere calculations to discuss the effects on both global and mesoscales on the three‐dimensional structure of the heliospheric magnetic field and their effects on galactic cosmic rays. These conclusions are in contrast to near‐solar‐minimum‐like heliospheric conditions that are currently assumed in modulation and transport calculations even during solar maximum. The expected complex heliospheric properties should be of major importance for the interpretation of the heliospheric boundary events observed by Voyager 1 since 2002. A companion paper by L. A. Fisk will explore the effects of the mesoscale structures on particle acceleration in the heliospheric boundary region. © 2004 American Institute of Physics