The Turkmen Carpet Museum is one of Ashgabat's most distinctive museums, focused on the woven patterns that carry tribal identity, status, and craft memory across Turkmen culture. The displays range from historic carpets to huge modern pieces, including rugs made as national showpieces rather than household objects.
It gives useful context for what you see in bazaars and official buildings around the country. Look less for a conventional art-museum narrative and more for repetition, symbolism, and technique: the guls, borders, colours, and dense handwork that turn a carpet into a kind of map of belonging.