By contrast, the principalities of Wales in the UK and Asturias in Spain, are not states today, although the independent mediaeval Welsh state was nonetheless referred to as the principality. In both cases, the heir to the country's throne is titular prince of the principality.
Sometimes the notion of a land as a principality is due to historical reasons: Catalonia, for instances, even when it was a sovereign state extending from Barcelona to Athens, was known as a principality, although its ruler was titled king (of the Kingdom of Aragón extended as the Aragonese Empire). It was a curious case where the ruling power had a nominal inferior degree to that of the ruled territory.
In the history of Russia the term "principality", and sometimes duchy, is used for render the Russian term knyazhestvo, a land ruled by a knyaz.