If you are flying in and out of the USA, Canada and Brazil the airlines apply the "piece" concept where an individual item's dimensions can't exceed 62". It's tough to pack a bike within that size unless it breaks down.

Everywhere else in the world the weight concept applies, where all they care about is the weight, and it is these ones where the bike box/bag is just regarded as part of your regular checked luggage (although there are plently of low cost carriers with severe weight restrictions and/or limit you to one bag).

Emirates are pretty good - economy class limit is still 30kg. So outside of the US/Canada you can travel with bike plus normal baggage without any fees.