Travelers who recall the ’90s heyday of sub-$300 round trips to Europe (taxes included) haven’t been happy in recent years, when a $1,000 flight began looking like a decent price. Their moods may improve now that one of Europe’s largest low-cost carriers is expanding in a big way, with new routes and inexpensive prices that could upend the transatlantic flight market as a whole.

Earlier this year, Norwegian Air Shuttle launched service connecting New York’s JFK airport to Oslo and Stockholm, and flights from Fort Lauderdale to Oslo, Stockholm, and Copenhagen. This week, the carrier announced service between Europe and three more American cities (Orlando, Oakland, Los Angeles) starting next year. A JFK-Copenhagen route is also on tap starting in February 2014.

Low-cost airlines tend to avoid long-haul flights, preferring to focus on shorter (and generally more lucrative) routes in the regions they know best. But for Norwegian, the transatlantic market was just too juicy to pass up. “We believe that the U.S is low-hanging fruit,” Norwegian CEO Bjorn Kjos said at a news conference on Tuesday, according to the San Francisco Chronicle. “People love to fly cheap and they love to fly far.”

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The airline will be using Boeing’s new 787 Dreamliner planes, which Norwegian thinks it can operate at a cost of 30% less than the usual long-haul aircraft. And at least when it first introduces service to its new U.S. cities, Norwegian’s prices will reflect those lower operating costs. Introductory fares from Los Angeles, Orlando, and Oakland to Scandinavia start at just $237 each way, taxes and fees included.

How good a flight price is that? Well, browsing at the website of Scandinavia’s large SAS airline, a round trip flight from Orlando to Oslo comes to a total of $993 during the low season of November. Included in that total is $588 in taxes and fees ($496 for an “international surcharge” alone). In other words, Norwegian Air Shuttle is charging less for a total round trip than what the traditional airline flight tacks on just in fees.

While the new routes will appeal most to American travelers interested in seeing Scandinavia (or Scandinavians interested coming to the States), it’s also easy to use Oslo or Stockholm as a jumping-off point to somewhere else in Europe, or even Russia. All that’s required is the booking of another low-cost flight overseas. Likewise, Norwegian has been thinking about partnering with an American carrier so that passengers could book a single ticket that would connect its hubs in Europe with dozens of U.S. cities. “It might be that we will work with low-cost operators like Jet Blue in the U.S.,” Kjos told Bloomberg in May. “Our passengers could fly to New York with us and continue with Jet Blue to other places in U.S.”

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As with any low-cost carrier, however, there are downsides to booking with Norwegian Air Shuttle. Unlike the typical airline with transatlantic service, which offers flights at least on a once-daily basis, Norwegian will generally fly each U.S.-Scandinavia route only two or three times weekly. So if you miss a flight, it may be a few days—or perhaps more than a week—until there’s another one that’s departing and actually has space for you. Also, Norwegian keeps fares low by following the Ryanair and Spirit Airlines business model, in which the only amenities beyond a basic seat cost extra. Passengers must pay up for things like checked baggage and food, of course, and there’s even a fee for using a credit card.