The Exploration Museum covers the full sweep of human exploration from the Norse settlement of Iceland and Greenland through the age of sail to the conquest of the poles and the Space Race. It sounds like a lot to pack into one building, but the curation is tight and the connections between eras — the same drive to push into the unknown, the same mixture of courage and recklessness — give the collection a genuine theme rather than just a miscellany of artefacts.
The Apollo astronaut training section is the most distinctive part of the museum and the reason most visitors seek it out. The connection between this small Icelandic fishing town and the Moon landings is so improbable that it has the quality of a good story even before you start reading the details. But the museum is also strong on the Norse explorer tradition, which is appropriate given that Húsavík itself was one of the first recorded European settlements in Iceland. Allow an hour to see it properly.