Pope Innocent III declared a crusade against the Cathars of Languedoc in 1208, after the murder of his legate Pierre de Castelnau, and the Albigensian Crusade opened in 1209 with the sack of Beziers, where a garrison commander is said to have been told to kill them all and let God sort out his own. Simon de Montfort led the campaign through Languedoc for the following decade, breaking the military power of the region's Cathar-tolerant nobility, most notably the counts of Toulouse, at battles including Muret in 1213. Royal French armies absorbed the crusade after Montfort's death in 1218, and the Treaty of Paris in 1229 formally transferred Languedoc's independent lordships to the French crown, ending Cathar communities' open political protection.
What the crusade could not finish, the Inquisition completed. Dominican inquisitors, working from Toulouse and Carcassonne through the thirteenth century, interrogated tens of thousands of believers, extracted genealogies of belief across whole villages, and burned perfecti at the stake, most infamously the two hundred or so taken at Montsegur in 1244 after a ten-month siege. Organised Cathar practice survived only in scattered, hunted pockets into the fourteenth century; Guilhem Belibaste, generally reckoned the last Cathar perfectus, was burned in 1321. Whether the church the inquisitors described this way, uniform, hierarchical and international, existed in that shape before their questioning gave it one is a live historiographical argument rather than a settled fact, and the atlas records it as such.