Unhygienix is out of fresh fish (as always), which is "shipped" overland in ox-drawn carts from Lutetia (Paris), and Getafix says that he needs some for his magic potion. Asterix and Obelix borrow a boat from Geriatrix and go fishing. After a storm, they get lost, but despite Obelix's concerns, they do not reach the edge of the world. Instead, they arrive on an island (North America) with delicious birds the Gauls call "gobblers" (turkeys), bears and "Romans" with strange facial paintings (Indians).
Soon they earn the "Romans"' affection, but they decide to leave after the "centurion" chooses Obelix as his rather rubenesque daughter's fiancé. They go to a small island. Seeing a boat coming, Asterix climbs a cairn of rocks holding a torch and a book to attract it. The crew are anachronistic vikings (with names like Herendethelessen, Steptøånssen, Nøgøødreåssen, Håråldwilssen, Irmgard, Firegård and their Huntingseåssen) - who managed a Pre-Columbian trans-oceanic contact and take the Gauls, whom they thought to be the local natives, to their homeland as proof that there are continents beyond Europe.
Their mutual desperation, the Gauls wanting to return home, and the vikings eagerness to prove their story of a new world, results in a trip back to Europe to the Vikings homeland. The vikings' chief, Ødiuscomparissen, greets them and was skeptical of their stories, until he saw the Gauls. They plan a celebration, then attempt to sacrifice the "natives" (much to the chagrin of the other vikings ("Why? They haven't done anything!")).
Before this can be carried out, a Gaulish prisoner called Catastrofix, who can understand both Gallic and Norse, stirs up Ødiuscomparissen's suspicion that Herendethelessen is a liar, causing a fight between the Vikings. Meanwhile, the Gauls escape. This escape is conducive to their original purpose, since Catastrofix is a fisherman and hence able to procure some fish for the magic potion. Unhygenix, however, prefers the scent of his own stock; a preference that explains why his product is such a delicate and filthy topic.
- The animated movie Asterix Conquers America, starring Craig Charles as the voice of Asterix, is based on this book. The most noticeable differences between the book and the film is that in the film, Getafix accompanies Asterix to America, and that the vikings do not appear in the film.
- When Obelix punches one of the attacking Native Americans K.O. the warrior first sees American-style emblematic eagles; the second time he sees stars in the formation of the American flag; the third time, he sees stars shaped like the United States Air Force roundel.
- Asterix' idea for getting the attention of the nearby Viking ship by holding up a torch references the Statue Of Liberty (which was a gift from France). In response Obelix states "I value my liberty".
- The idea that Vikings reached America centuries before Columbus is one that was seriously considered at the time and is now seen as fact. However, the Vikings landed in America around 1000 C.E., roughly a thousand years after the time period in which Asterix is set.
- When the Vikings set foot on American ground Herendethelessen paraphrases Neil Armstrong's famous quote: "It's one small step for (a) man, one giant leap for mankind."
- The nationality of the Vikings in this story is Danish (The Vikings from the earlier album, Asterix and the Normans, were Norse).
- This is made clear by several references to William Shakespeare's play about the Danish prince Hamlet. Odiuscomparissen at one point says: "Something is rotten in the state of ..." while holding a skull in his hand. In the play, the character Marcellus claims "something is rotten in the state of Denmark", and Hamlet delivers a monologue on death while holding the exhumed skull of his childhood playmate, the court jester Yorick. Towards the end of the comic Herendethelessen is seen wondering if he is a discoverer or not? He concludes by quoting Hamlet: "To be or not to be, that's the question."
- When the Viking's village is in sight, Herendethelessen tells his crewmembers to get ready to be covered with honors only for them to be greeted by an angry booming voice. Steptøånssen remarks that it is their fearsome chief Odiuscomparissen, to which Herendethelessen tells him that it certainly is not a mermaid — a reference to the statue The Little Mermaid in the port of Danish capital Copenhagen.
- Herendethelessen's dog, Huntingseåssen, is a Great Dane.
- Pseudo-Danish spelling is used for the Viking's speech.