Historical evidence of solar variability is based upon sunspot occurrence and rotation rates, and on observations of the Sun's radius. I present here the methods of observation used to this end, and assess their accuracy and limitations. I then discuss and interpret the periodicities I have found. The main conclusions are that, during the past three centuries solar variability has appeared in the form of recurrent expulsions of magnetic activity at the Sun's surface, accompanied by a modulation of its rotation and periodic changes in its radius. Periodicities of from 150 days up to as much as 80 years, including the well-known 11-year cycle, are present in the historical observations and contemporary observations. No exact theoretical model of the change in solar radiation output under the influence of periodic magnetic fields has yet been developed; but the presence of periodicities common to the Sun's activity and to the Earth's environment suggests a causal relation between solar variability and the meteorology of the Earth.