In the British peerage, a royal duke is a duke who is a member of the British Royal Family, entitled to the style of His Royal Highness. Royal dukedoms are the highest titles in the British roll of peerage. They are titles created for legitimate sons and male line grandsons of the British monarch, usually upon reaching their majority or marriage. The titles can be inherited but cease to be "royal" once they pass beyond the grandsons of a monarch. As with any peerage, once the title becomes extinct, it may subsequently be recreated by the reigning monarch at any time.
In the United Kingdom, there is nothing intrinsic to any dukedom that makes it "royal". Rather, these peerages are called royal dukedoms because they are created for, and held by, a member of the royal family who is entitled to the style Royal Highness. Although the term "royal duke" therefore has no official meaning per se, the category "Duke of the Blood Royal" was acknowledged as a rank conferring special precedence at court in the unrevoked 20th clause of the Lord Chamberlain's order of 1520. This decree accorded precedence to any peer related by blood to the sovereign above all others of the same degree within the peerage. The order did not apply within Parliament, nor did it grant precedence above the Archbishop of Canterbury or other Great Officers of State such as is now enjoyed by royal dukes. But it placed junior "Dukes of the Blood Royal" above the most senior non-royal duke, junior "Earls of the Blood Royal" above the most senior non-royal earl (cf. Earldom of Wessex), etc. It did not matter how distantly related to the monarch the peers might be (presumably they ranked among each other in order of succession to the Crown). Although legally "time does not run against the King", so that the 1520 order is theoretically still in effect, in fact the "Blood Royal" clause seems to have fallen into desuetude by 1917 when George V limited the style of Royal Highness to children and male-line grandchildren of the Sovereign. Thus peers of the blood royal who are neither sons nor grandsons of a sovereign are no longer accorded precedence above other peers.