The role of head of state in the United Kingdom is held by the Sovereign; the present Sovereign is Queen Elizabeth II.
Succession to the throne
As a hereditary monarchy, the rules for succession to the throne are established by common law, as modified by statute.
In accordance with the Act of Settlement (1701), on the death of the Sovereign he or she is succeeded by his or her "heir of the body"; this operates in accordance with the principle of male-preference primogeniture. If the Sovereign has only one child, that child succeeds. If there are more than one children, then the order of succession is determined first by sex, and then by age. The oldest son always succeeds, even if he has a sister who is older than him.
If the Sovereign dies childless ("without issue") then the order of succession is applied to their siblings: the oldest surviving brother then succeeds, even if he has a sister who is older than him. If the Sovereign's siblings have died before he or she died, then the order of succession works through the sons and daughters of the next oldest deceased brother, and so on.
Only legitimate children are able to succeed. The Royal Marriages Act 1772 operates to restrict the capacity for a potential heir to marry without the Sovereign's approval: all descendants of King George II, other than women who have married into foreign families, are required to obtain the Sovereign's consent before marrying, unless they can otherwise obtain approval from both Houses of Parliament.
The Bill of Rights (1689) and Act of Settlement require all heirs to be descendants of Sophia, Electress of Hanover (d. 1714), and impose further requirements that an heir be a Protestant, that they may never have married a Roman Catholic, and that they be in full communion with the Church of England. Heirs not meeting these conditions are skipped over as if "naturally dead".
The role of the Sovereign beyond the United Kingdom
As Sovereign in right of the United Kingdom, the Sovereign is also head of state in the "Crown dependencies" of Jersey, Guernsey (and its dependencies), and the Isle of Man. While the external relations of these islands is dealt with by the United Kingdom, however, they do not form part of the United Kingdom itself, and have their own constitutional arrangements.
Similarly, the United Kingdom has sovereignty over various territories around the world, known as the British overseas territories. As such, the Sovereign is also head of state in these territories, although again these do not form part of the United Kingdom itself, and have their own constitutional arrangements.
The British Sovereign is also the Sovereign of certain other Commonwealth Realms: Antigua and Barbuda, Australia, the Bahamas, Barbados, Belize, Canada, Grenada, Jamaica, New Zealand, Papua New Guinea, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, the Solomon Islands and Tuvalu. Each of these nations is a separate monarchy; the Sovereign therefore holds sixteen different crowns. In each nation, the Sovereign is represented by a Governor-General, who generally stands in relation to the local government in the same relation as the Sovereign does to the British government.
Finally, the Sovereign has the title Head of the Commonwealth. The Commonwealth is a body of nations mostly made up of former colonial dependencies of the United Kingdom. The role of Head of the Commonwealth is a personal role of the present Queen, Elizabeth II, and is not formally attached to the monarchy itself (although the present Queen's father, King George VI, also held the title). The role is purely a ceremonial one.
While the members of the Sovereign's family do not have any role in government, they do exercise ceremonial functions on his or her behalf.
A male Sovereign has the title "King", while a female Sovereign is the "Queen". The wife of a King is also known as a Queen; however, the husband of a female Sovereign has no specific title.
By convention, the Sovereign's eldest son is created "Prince of Wales" and "Earl of Chester" while still a boy; he also automatically gains the title of "Duke of Cornwall". Also by convention, the Sovereign's sons receive a peerage either upon reaching the age of twenty-one, or upon marrying.
The style of Prince or Princess extends to the children of the Sovereign, the children of the sons of the Sovereign, and the eldest son of the eldest son of the Prince of Wales. Furthermore, wives of Princes are styled Princesses, though husbands of Princesses do not automatically become Princes.