I heard and read about other airlines but not about Norwegian. I read their website and searched for articles, blog posts but there is nothing I can find.
Do they overbook flights?
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It is well settled that it is legal for an airline to overbook flights, and the EC261 compensation rules even makes it definite and knowable to the airline how much it will cost them to guess wrong about the number of no-shows -- thereby enabling a crisp business-driven decision about how much to overbook each particular flight.
The only possible reason an airline would have not to overbook is that they would be able play this up heavily in their marketing, hoping that passengers concerned about being bumped would choose to fly with them rather than a competitor.
Since Norwegian are not in fact bragging loudly about how they don't overbook, it seems safe to assume that they do in fact overbook.
Yes, as probably every other airline, Norwegian is also overbooking their flights.
They have in the past months received quite a lot of negative press in Norway about this issue. Since all Norwegian's 737 MAX airplaines are currently grounded, they are also regularly flying replacement aircrafts with less seats than originally anticipated and the situation is quite tense.
Being denied boarding by Norwegian may have more significant impact than with other airlines. On many routes, Norwegian have very infrequent departures, so being bumped to the next departure may mean that you are stuck for a day or more. You can not assume that Norwegian will transfer you to a flight operated by other airlines.
The whole overbooking concept is tightly linked to flexible fares, mostly used by business travellers who change their plans frequently and late, which may leave the airline with many empty and unpaid seats. That's the reason airlines overbook: they need to have someone in that seat so they can get paid.
Low-cost carriers usually overbook a lot less than incumbents because many of their fares are non-refundable and non-modifiable or attract high penalties for cancellations or changes, so whether the passenger actually flies or not, they have paid their seat, and there's no need to "replace" them.
However, even though in the beginning of LCCs fares were non-refundable and overbooking wasn't needed, the lines have blurred a bit, so it's possible for them to overbook, though this should be in very small numbers (remember that it will cost them dearly if they have to bump someone now).
Note that any airline, even if they don't normally overbook, may end up in situations that have the same effect as overbooking:
So whatever the airline, you may end up being refused boarding. That's where EC261 comes in :-)