Solar Dynamo theory is concerned with the origin of the solar magnetic field. It is an exciting time for research into the solar dynamo - the problem of the origin of the sun's magnetic activity. The beginning of the new Millennium has seen great increases in both theory (made possible by the breathtaking advances in computational power) and high resolution observations (driven by the recent and planned space missions). Taken together, these advances have significantly increased our understanding of the magnetic activity and variability of our nearest star. The well-known eleven-year sunspot cycle is a manifestation of solar magnetic activity. Sunspots are cool dark patches on the solar surface which are associated with strong magnetic fields. They appear at mid-latitudes at the start of a cycle and migrate to the equator. Solar magnetic activity has been recorded since the early 17th Century following the invention of the telescope and the activity record can be extended back thousands of years using proxy data. These data (which include Beryllium records in ice-cores and Carbon records in tree rings) indicate that solar magnetic activity has switched off' for periods of up to 200 years in the past. One such period of reduced activity called the Maunder Minimum occurred in the 17th Century when astronomers would report excitedly on any sunspots which appeared. These periods of reduced activity are known as Grand Minima. It is intriguing to note that the Maunder Minimum of solar magnetic activity coincided with the ''Little Ice Age'' - a period when the global terrestrial temperature was reduced. Indeed the possible links between solar variability and climate is a field of active research. Explaining the origin of the sun's magnetic field is the fundamental problem of solar magnetohydrodynamics. This field underlies all solar magnetic phenomena such as solar flares, coronal mass ejections and the solar wind, and is responsible for heating the solar corona to such high temperatures. These phenomena may all have important terrestrial impacts, causing severe magnetic storms and major disruption to satellites, as well as having a possible impact on the terrestrial climate.