The new building opened on 10 October 2014, sixteen thousand square metres organised around a single broad central staircase, with landscape work by Kristine Jensens Tegnestue. The logic is vertical: upper levels carry changing exhibitions of history and culture from around the world, lower levels hold the permanent displays of Danish, Scandinavian and European prehistory. The permanent galleries run the Stone Age, Bronze Age, Iron Age and Viking Age as they unfolded in Denmark, then Medieval Denmark from roughly 1050 to 1536. They are heavily interactive and offered in several languages, built to be readable by a nine-year-old without patronising an archaeologist. In 2018 the museum drew 368,656 visitors.

The museum was founded in 1970 and works closely with the archaeology and anthropology departments of Aarhus University, which is how a regional institution ended up with an ethnographic collection of nearly fifty thousand objects from around the world, plus photographs, film and sound recordings. But the crowds come for the Danish material. Grauballe Man, the best-preserved bog body in the world, lies here — his own story is told at Grauballe, where he was found. Thousands of items from the great Iron Age weapon deposits at Illerup Ådal fill another gallery — a story large enough to stand on its own. Seven local runestones stand in the building, among them the Mask Stone; so does the Snaptun stone, whose carved face is often identified as Loki. There are copies of the Golden Horns of Gallehus and a model of the great Bronze Age barrow at Borum Eshøj.

On a rise just southeast of the museum stands a stave church, and everything about it is an argument. Not one original Danish stave church survives. In 1960, excavators working beneath the present church at Hørning, near Randers, found a floor and a pattern of post-holes from a Viking Age building — small by later standards, roughly nine metres by five. One physical piece had turned up earlier: in 1887, during repairs to the walls of the standing church, workers found a section of the hammer-beam, the horizontal timber under the roof projection that held the vertical planks. Its outer face is carved with writhing serpents in the late Viking manner, and it is now in the National Museum of Denmark. Tree rings in the timber date the building to about 1060, right on the seam between the Viking Age and the Middle Ages. Moesgaard built the reconstruction from that evidence, added a bell frame where the excavation showed one had stood, and cast the bell on site following a nine-hundred-year-old written description — a replica of the almost eight-hundred-year-old bell at Smollerup church near Viborg.

The estate runs to a hundred hectares of park, forest, field and shoreline, dropping from the museum to the Bay of Aarhus, and the Prehistoric Trail threads four kilometres of it, marked by white stones with a red dot. It starts in the baroque manor park, laid out in the 1770s, and crosses a field where stone burial chambers from various parts of Denmark have been relocated and rebuilt after development destroyed their original sites — Gotland sheep graze it in summer to keep the vegetation down. Past the old watermill and the ruin of a long barrow, the path enters ancient woodland and a forest swamp crossed on a footbridge. Then comes the Prehistoric Forest, planted by the museum in 1964 and divided into the successive Danish forest types since the ice retreated: birch and pine, hazel and pine, early lime, late lime, and finally beech, which has held since about 700 BC. The beech section ends at the beach. On the way back stands a reconstructed Iron Age farmhouse, sixteen metres long, based on a settlement at Tofting just south of the German border, where humans and cattle wintered under one roof.

The manor house at the top of the estate was built between 1780 and 1784 for a Gyldenkrone baron, on plans by the architect Christian Joseph Zuber. Århus County bought the manor and its land in 1960, and the old house now holds university departments rather than a family. Down in Moesgaard Skov, a timber-framed water mill called Skovmøllen sits on the Giber Å stream; the earliest reference to it is from 1590, the buildings were rebuilt with an overshot wheel in 1785, and a storey was added in 1852. Milling stopped in 1910, but the machinery still works as both saw and granary mill, and there is a restaurant in it now. Somewhere in the park, entirely out of period and entirely welcome, stands a century-old wooden house from Ayutthaya, the old capital of Siam, given to the museum by Thailand in 1975.