She is usually depicted as a woman who is a serpent or fish (much like a mermaid) from the waist down. She is also sometimes illustrated with wings, two tails or both, and sometimes referred to as a nixie.
The most famous literary version of Melusine tales, that of Jean d'Arras, compiled about 1382 - 1394 was worked into a collection of "spinning yarns" as told by ladies at their spinning.
The tale was translated into the English language c. 1500, and often printed in both the 15th century and the 16th century. (There is also a prose version called the Chronique de la princesse.)
It tells how Elynas, the King of Albany (a poetical euphemism for Scotland) went hunting one day and came across a beautiful lady in the forest. She was Pressyne, mother of Melusine. He persuaded her to marry him but she agreed, only on the promise — for there is often a hard and fatal condition attached to any pairing of fay and mortal — that he must not enter her chamber when she birthed or bathed her children. She gave birth to triplets. When he violated this taboo, Pressyne left the kingdom, together with her three daughters, and traveled to the lost Isle of Avalon.
The three girls — Melusine, Melior, and Palatyne — grew up in Avalon. On their fifteenth birthday, Melusine, the eldest, asked why they had been taken to Avalon. Upon hearing of their father's broken promise, Melusine sought revenge. She and her sisters captured Elynas and locked him, with his riches, in a mountain. Pressyne became enraged when she learned what the girls had done, and punished them for their disrespect to their father. Melusine was condemned to take the form of a serpent from the waist down every Saturday.
Raymond of Poitou came across Melusine in a forest in France, and proposed marriage. Just as her mother had done, she laid a condition, that he must never enter her chamber on a Saturday. He broke the promise and saw her in the form of a part-woman part-serpent. She forgave him. Only when, during a disagreement with her, he called her a "serpent" in front of his court, did she assume the form of a dragon, provide him with two magic rings and fly off, never to return.
Melusine legends are especially connected with the northern, most Celtic areas of Gaul and the Low Countries. Sir Walter Scott told a Melusine tale in Minstrelsy of the Scottish Border (1802 -1803) confident that
When Count Siegfried of the Ardennes bought the feudal rights to Luxembourg in 963, his name became connected with the local version of Melusine. In 1997 Luxembourg issued a postage stamp commemorating this Melusina, with essentially the same magic gifts as the ancestress of the Lusignans. This Melusina magically made the castle of Bock appear the morning after their wedding. On her terms of marriage, she too required one day of absolute privacy each week. Alas, Sigefroid, as the Luxembourgeois call him, "could not resist temptation, and on one of the forbidden days he spied on her in her bath and discovered her to be a mermaid. When he let out a surprised cry, Melusina caught sight of him, and her bath immediately sank into the solid rock, carrying her with it. Melusina surfaces briefly every seven years as a beautiful woman or as a serpent, holding a small golden key in her mouth. Whoever takes the key from her will set her free and may claim her as his bride." 
Martin Luther knew and believed in the story of another version of Melusine, die Melusina zu Lucelberg (Lucelberg in Silesia), whom he referred to several times as a succubus (Works, Erlangen edition, volume 60, pp 37–42). Johann Wolfgang von Goethe wrote the tale of Die Neue Melusine in 1807 and published it as part of Wilhelm Meisters Wanderjahre. The playwright Franz Grillparzer brought Goethe's tale to the stage and Felix Mendelssohn provided a concert overture "The Fair Melusina," his Opus 32.
Melusine is one of the pre-Christian water-faeries who were sometimes responsible for changelings. The "Lady of the Lake", who spirited away the infant Lancelot and raised the child, was such a water nymph. For other European water sprites dangerous to humans, especially men, see Lorelei, Nixie.
"Melusina" would seem to be an uneasy name for a girl-child in these areas of Europe, but Ehrengard Melusine von der Schulenburg, Duchess of Kendal and Munster, mistress of George I of Great Britain, was christened Melusine in 1667.
Melusine is sometimes used as a heraldic figure, typically in German and Scandinavian Coats of arms, where she supports one scaly tail in each arm. She may appear crowned. The Coat of Arms of Warsaw features a siren (identified in Polish as a syrenka) very much like a depiction of Melusine, brandishing a sword and shield. She is the water-spirit from the Vistula who identified the proper site for the city to Boreslaus of Masovia in the late 13th century.
A stylized cartoon version of a siren, which is similar to some of the Melusine legends, serves as the mascot that appears in the Starbucks logo to advertise the coffee chain. In fiction, the Melusine legend is part of A.S. Byatt's Possession. One of the main characters, Christabel LaMotte, writes an epic poem about Melusina.