The Swedes were generally unhappy with this union, called the Union of Kalmar, and over the next century they instead followed the rule of regents and even elected a counter-king, Karl II. Finally the union was overthrown in 1523 by Gustav I Vasa, who became their new king. Under strong rulers Sweden became a major European power in the 17th-century.
In 1818 Karl XIV Johan, one of Napoleon's marshals, was chosen to be king. His line has ruled since that time, though the powers of the monarchy are now largely ceremonial.
Note that there are some numbering inconsistencies. Kings Eric XIV and Karl IX adopted their numbers based on a legendary history of Sweden. Their predecessors of the same names were posthumously given numbers by counting backwards.