The Ascension of House Atreides can be traced to the marriage of Paul Atreides to Princess Irulan Corrino after the Fremen defeat of the Sardaukar on the Plains of Arrakeen. Irulan Corrino was the eldest daughter of Shaddam Corrino IV, who had been utterly defeated in the Arrakis Revolt.
Other rival claims to the Golden Lion Throne were either destroyed with House Corrino, joined the new Emperor Paul, or their animosity did not surface until later. Powerful House Harkonnen, who had been allied with House Corrino, was destroyed concurrently on the desert world.
House Thorvald's rebellion against Paul Muad'Dib began in 10,194 AG, with Paul's speech before the Landsraad after the Fremen sack of Kaitain. As Paul spoke to the nobles, Earl Memnon Thorvald shouted demonstratives at Paul, as he marched out of the Assembly Area. Thorvald scored some minor victories, but Paul's Jihad marched inexorably forward. Four years later, when Thorvald planned to detroy the populace of Caladan, and take Lady Jessica hosatge; Paul ordered Thorvald's homeworld of Ipyr sterilized.
Another powerful House, House Vernius of Ix, was embittered towards House Atreides, but led by under-siege noble, Bronso of Ix; whose animosity towards Paul's rule did not openly surface until the early 10,200s. Alia Atreides, as Regent, captured Bronso, and had him executed in 10,201 AG.
Even with the first Corrino threat of Shaddam's ghola army, which attacked openly during Alia's Regency; and the second threat under Wensicia Corrino against Paul's newborn children, Leto Atreides II and Ghanima, the Atreides survived, and Leto II became Emperor. From that time through the death of Leto II, approximately 3,500 years later, Atreides Empire dominated the Known Universe.