This volume, the proceedings of an ISSI workshop 21-26 March 1999, Bern, Switzerland summarizes the results from the detection of cosmic rays at the surface and in the lower atmosphere of Earth during the 50 years since the invention of the neutron monitor by John A. Simpson in 1948. The properties of solar and galactic cosmic rays in the heliosphere, such as Forbush decreases, modulations by solar and heliosphere parameters, the physical processes that govern them, and their connection to Space Weather, are reviewed. This interdisciplinary compilation provides links between cosmic ray physics, geophysics, terrestrial climate, and human activity and health.