The Quran

وَاذكُروا إِذ جَعَلَكُم خُلَفاءَ مِن بَعدِ عادٍ وَبَوَّأَكُم فِي الأَرضِ تَتَّخِذونَ مِن سُهولِها قُصورًا وَتَنحِتونَ الجِبالَ بُيوتًا ۖ فَاذكُروا آلاءَ اللَّهِ وَلا تَعثَوا فِي الأَرضِ مُفسِدينَ

Muhammad Asad

"And remember how He made you heirs to [the tribe of] 'Ad¹ and settled you firmly on earth, so that you [are able to] build for yourselves castles on its plains and hew out mountains [to serve you] as dwellings:² remember, then, God's blessings, and do not act wickedly on earth by spreading corruption."

Cf. the parallel expression in verse 69 above - "heirs to Noah's people" - and the corresponding note. From all the historical references to the Thamud it is apparent that they were one of the greatest and most powerful Arab tribes of their time.
A reference to the elaborate rock-dwellings or tombs - to be seen to this day - which the Thamud carved out of the cliffs west of Al-Hijr, in northern Hijaz, and embellished with sculptures of animals as well as many inscriptions attesting to the comparatively high degree of their civilization and power. In popular Arabian parlance, these rock-dwellings are nowadays called Mada'in Salih ("The Towns of Salih").