Note: At the end there are explanations of some terms that might not be clear from reading the below.
Originally Posted by Next Star
What happened to the Duke of Burgundy and the rest of the ducal family are there are any descents still alive or did the family line die out?
The Duchy of Burgundy 'belonged' to several Houses.
The first Duke of Birgundy was Richard the Justiciar, from the House of Ardennes
. After the last descendant of the dynasty, Otto-Henry (the Great) died without male heirs, Burgundy was inherited by his step-son, Otto-Willelm. However in 1004 (?) the Duchy of Burgundy was annexed to the Crown of France by King Robert II of France (Robert was the son of Hugh Capet and Otto-Henry was Hugh Capet's younger brother. Therefore Robert was the legitimate heir.) However though Otto-Willelm was deprived of actual Dukedom of Burgundy, he continuted to reign over the so-called free County of Burgundy. There were 3 counts, if I'm not mistaken, after which it was mered with the Dukedom again.
Robert II belonged to the House of Capet
(he was Hugh Capet's son), therefore the second house that 'owned' the Duchy was the Capetian. He was succeded by Henry I, who was also the Duke of Burgundy (and the last Capetian Duke). Robert, aided by his mother, rebelled against Henry and the peace was achieved only when he was given the Dukedom of Burgundy, thus establishing the House of Burgundy.
The last Duke of the House of Burgundy
was Philip I, Duke of Burgundy. Philip was not only Duke of Burgundy (inherited from his grandfather) but also Count of Burgundy and Artois (inherited from his grandmother). He married Maragret (heiress of Flanders) however died in the same year (of plague), without heirs.
The Duchy was inherited by the closest living relative (paternal line), King John II of France (the county was inherited by someone else from his maternal line).
After John II inherited the Duchy (1361), the third House gained the possession of it - the House of Valois
. The House of Valois owned the Dukedom untill 1482. The last Duke of Burgundy, Charles I the Bold had only 1 surviving daughter, Mary. After his death Mary became the Duchess of Burgundy.
In 1477 Mary was made to sign the charter of rights, called the Great Privilege (?). According to the charter the provinces of Flanders, Brabant, Holland and Hainaut (major parts of Burgundy) retained all the local and community right. Basically the Dukedom of Burgundy stopped existing ever since. Parts of it were annexed by France. Mary retained only small parts of the original Duchy.
She married to Archduke Maximilian of Austria (later Maximilian I, Emperor of the Holy Roman Empire). That's how the Low Countries came to the Habsburgs
, starting a contention between France and the Habsburghs (later Spain and then Austria) for 3 centuries. The contention reached its highest point during the War of the Spanish Succession.
After Mary's death, Louis XI of France forced Maximilian to agree to the Treaty of Arras, by which Franche Comte and Artois passed to French rule. Later Franche Comte and Artois were changed for the County (not Duchy) of Burgundy and Picardy by the Treaty of Senlis (spelling?).
Basically Mary was the last Duke (Duchess) of the Burgundy. Her son, Philip I of Castile, inherited only the Burgundian Netherlands
(though still quite a big part of the former Duchy). His sucessors inherited the Burgundian Netherlands as well until at some point there were divided between and invaded by various countries (France, Netherlands, Germany, Luxembough, Belgium).
*Burgundian Netherlands - Union of 17 Provinces, covering (roughly) the current Netherlands, Belgium, Luxembourgh and parts of France (and a part of Germany, if I'm not mistaken).
* Low Countires - Historical region of de Nederlanden
* De Nederlanden - not to confuse historical Netherlands (covering most of the Burgundian Netherlands, including Low countires) and current country (which occupies only part of the historical one), the Dutch speakers usually speak of Nederland (singular) for the current country and de Nederlanden for the historic part. In English (roughly) Netherland (or Holland) for the current country, the Netherlands (plural) for the historic one.