She was the daughter of Pelias, king of Iolcus. In the story, many suitors appeared before King Pelias, her father, when she became of age to marry. It was declared she would marry the first man to yoke a lion and a boar to a chariot. The man who would do this, King Admetus, was helped by Apollo, who had been banished from Olympus for 9 years to serve as a shepherd to Admetus. With Apollo's help, Admetus completed the king's task, and was allowed to marry Alcestis. After the wedding, Admetus forgot to make the required sacrifice to Artemis, and found his bed full of snakes.
Apollo again helped the newly wed king, this time by making the Fates drunk, extracting from them a promise that if anyone would want to die instead of Admetus, they would allow it. Since no one volunteered, not even his elderly parents, Alcestis stepped forth. Shortly after, Heracles rescued Alcestis from Hades, as a token of appreciation for the hospitality of Admetus. Admetus and Alcestis had a son, Eumelus, a participant in the siege of Troy, and a daughter, Perimele.
Alcestis gives her life for Admetus. Painting by Friedrich Heinrich Füger, 1751-1818. Gemäldegalerie der Akademie der bildende Künste, Wien