Recent analysis of historical records of geomagnetic activity has revealed that there has been a major change in the magnetic field in the solar corona over the past 150 years: specifically, the total magnetic flux leaving the Sun and entering the heliosphere has more than doubled since 1900. This change is found to be consistent with a 35% rise deduced from space measurements since they began in 1963 and with the abundances of various isotopes produced in ice sheets, tree-rings and meteorites by cosmic ray bombardment. Furthermore, modelling of magnetic flux emergence from the Sun has reproduced the observed variation very closely. This magnetic field permeates all of the heliosphere and protects Earth from galactic cosmic rays. The change observed corresponds to a fall in average fluxes of cosmic rays by 15% at energies above 3 GeV and by 5% at >13 GeV. These changes, and/or associated changes in solar irradiance, may have had a number of effects on the Earth's climate. We will review the possible effects on the global electric circuit, on global cloud cover and on the radiative forcing of the Earth's climate system. We will also demonstrate why it is vital that we understand all elements of the solar contribution to climate change so that the magnitude and temporal gradient of the anthropogenic contribution can be quantified.