The Crown dependencies have an anomalous constitutional status:
• They are neither parts of the United Kingdom nor British colonies (or British Overseas Territories, to use the modern parlance); but they are British possessions [Interpretation Act 1978, Sch 1]. Their citizens are British citizens.
• The UK is responsible for the dependencies' external affairs, but they are not within the EU.
• The dependencies are nominally governed by Lieutenant Governors appointed by the Queen. When taking political decisions regarding the dependencies, the Queen acts through the Privy Council and its special committees for the Channel Islands and the Isle of Man.
• The UK Parliament claims the right to legislate for the dependencies (though there is some dispute in the dependencies themselves about this). However, UK statutes do not apply to them by default.
• The dependencies have their own domestic legislatures.
Sir William Anson wrote in in The Law and Custom of the Constitution:
The Isle of Man has been in allegiance to the English Crown since the reign of Henry IV.... From the reign of Henry IV until 1735, with an interval during Elizabeth's reign, it was held of the Crown in fee by the House of Stanley. The tenure was on terms of doing homage and presenting two falcons to King or Queen at the Coronation. It then passed by inheritance to the Dukes of Athole, by whom the feudal rights were sold to the Crown in 1765, with a reservation of certain manorial rights and of the ecclesiastical patronage. These were bought by the Crown in 1829.The vesting of the island in the Crown was accomplished by the Isle of Man Purchase Act 1765 (now repealed).
The history of Crown sovereignty over the Channel Islands was outlined in the 1953 judgment of the International Court of Justice in the Minquiers and Ecrehos Case:
The United Kingdom Government derives the ancient title invoked by it from the conquest of England in 1066 by William, Duke of Normandy. By this conquest England became united with the Duchy of Normandy, including the Channel Islands, and this union lasted until 1204 when King Philip Augustus of France drove the Anglo-Norman forces out of Continental Normandy. But his attempts to occupy also the Islands were not successful.... On this ground the United Kingdom Government submits the view that all of the Channel Islands... remained, as before, united with England and that this situation of fact was placed on a legal basis by subsequent Treaties concluded between the English and French Kings.A more recent judgment of the UK Supreme Court tells a similar story (R (Barclay) v Secretary of State for Justice  UKSC 9):
The Channel Islands consist of two Bailiwicks, Jersey and Guernsey. When King Philippe Auguste retook possession of continental Normandy in 1204, King John retained the Channel Islands. His right as Duke of Normandy lapsed, and a separate title grew up by force of occupation, which attached to him as King of England. This was confirmed by the Treaty of Bretigny in 1360....The existence of the "separate title" referred to here seems to be a matter of some unclarity. The English monarchy acknowledged the loss of the Duchy of Normandy in the Treaty of Paris (1259), but to this day the Queen is accorded the title 'Duke of Normandy', and the publicly stated position of the monarchy is that the Islands "owe allegiance to The Queen in her role as Duke of Normandy". Guernsey has quite recently been described in a Privy Council judgment as "part of the original Duchy of Normandy" (Jersey Fishermen's Association Ltd v States of Guernsey  UKPC 30).
The UK does not normally legislate unilaterally for the Crown dependencies. The Privy Council stated in Jersey Fishermen's Association:
It is accepted that Her Majesty in Council could in theory legislate without any initiative from the Bailiwick [of Guernsey], but in practice there would be prior consultation with the Bailiwick.Likewise, it was stated in Barclay:
By convention Parliament does not legislate for the Islands without their consent in matters of taxation or other matters of purely domestic concern.... It is the practice for the Island authorities to be consulted before an international agreement is reached which would apply to them.The States of Jersey Law 2005 recognised this internal autonomy, and added that it was increasingly necessary to extend this freedom to external affairs:
WHEREAS it is recognized that Jersey has autonomous capacity in domestic affairs;
AND WHEREAS it is further recognized that there is an increasing need for Jersey to participate in matters of international affairs....
In recent times, politicians in the Channel Islands have toyed with the idea of full independence from the British crown. The independence debate in Jersey and Guernsey is to be seen in the context of concerns that British interference will threaten the islands' livelihood as offshore financial centres.
For many years now, there has been an active Manx nationalist movement which campaigns for independence from the British crown, but the prospects of an independent Isle of Man emerging in the near term seem slim.