Hanoverian succession
Established by the Act of Settlement (1701). In order to prevent James Edward Stuart, the Catholic son of James II, to become king, the line of succession was passed on to Sophia of Hanover and her heirs. After Queen Anne's death, George I succeeded her in 1714. The Personal Union of the English and Hanoverian monarchy lasted from 1714 until 1837 when Queen Victoria inherited the throne.
Establishing the Hanoverian succession
The establishment of the Hanoverians as British monarchs is a consequence of the changes following the Glorious Revolution. William III and Mary were made joint rulers with the Parliament's consent. The Bill of Rights stipulated that Catholics cannot be monarchs. After William's death in 1702, Mary's sister Anne became queen, whose last surviving child had died in 1700. Although the Bill of Rights prevented already the succession of Catholics, the Act of Settlement (1701) was to drown all claims of potential Catholic successors. Before that, about 50 members of the Catholic Stuart branch could raise a claim to the throne. The first in line would have been James Francis Edward Stuart, son of James II. As he was a Catholic, however, this scenario was unacceptable for the Protestant elite. Instead it was decreed in the Act of Settlement that Electress Sophia of Hanover and her heirs were to inherit the throne provided they were not Catholic. Sophia was the - of course Protestant - granddaughter of James I.
In June 1714, Sophia died and her son George Louis became Elector of Brunswick and the heir apparent to the British throne. Only two months later, Queen Anne died and George Louis succeeded her as George I. This marks the beginning of the Hanoverian line.
End of the Personal Union
The Personal Union between Britain and Hanover ended when Victoria came to the throne in 1837. In Hanover, women could neither inherit the electorate (Kurfürstentum) nor the later Kingdom of Hanover. Therefore, Hanover fell to Victoria's uncle Ernest Augustus.
Sources
Simms, Brendan. The Hanoverian Dimension in British history. Cambridge: Cambridge University Press, 2007.
Wende, Peter. Englische Könige und Königinnen der Neuzeit. München: C.H.Beck, 2008.