Madame Tussauds began as the travelling wax exhibition of Marie Tussaud (born Marie Grosholtz, 1761–1850), a French sculptor who learned her craft in Paris and later settled in London, where she opened a permanent museum in 1835.  Its present London building on Marylebone Road dates from 1884, replacing the original Baker Street premises, and has since been rebuilt and extended after a major fire in 1925 and wartime damage in 1940.
 
Marie Grosholtz was born in Strasbourg in 1761 and trained under the physician and wax modeller Philippe Curtius, who taught her to create lifelike wax portraits and anatomical models.
 
During the French Revolution , like many artists of the period, she was drawn into making death masks of executed figures—an experience that later fed directly into her famous “Chamber of Horrors.”
 
In 1802 she took her exhibition to Britain and, because of the Napoleonic wars, remained there, touring the British Isles for more than three decades as a showwoman with her wax figures.
 
Interesting fact...
Many of the wax heads and mutilated bodies in the original Chamber of Horrors were modelled directly from actual severed heads and corpses. Tussaud using casts and death masks made during and after the French Revolution.  This gave the gallery its unnerving realism and moral shock value - nice!