How do whales cope with deep diving?

The main problem at depth is that the increased pressure pushes more nitrogen gas from the lungs into solution in the blood and tissues...

Whales and other deep-divers are generally untroubled by this because they are adapted to remain submerged for extended periods of time, using only the oxygen already present in their bodies. Humans, on the other hand, need to use scuba gear, meaning we end up breathing compressed air, which must be delivered under pressure to compensate for the increased ambient water pressure at depth.

Consequently, the increased density of the air consumed by a diver means that significantly more nitrogen dissolves in the blood and tissues. When a whale resurfaces, it generally does so slowly, giving plenty of time for reequilibration and redistribution of the dissolved nitrogen. 

The scuba diver breathing normal air, on the other hand, surfaces relatively rapidly and also carries a much larger dissolved nitrogen load. Beyond a certain depth, this makes the bends inevitable, unless decompression steps are included during surfacing. Also, at higher pressures, the dissolved gases also act as anaesthetic agents, causing nitrogen narcosis, which is why divers going really deep using a helium oxygen mix instead.

The other benefit of helium is that it is much lower density than nitrogen, so even under pressure the drag felt by the gas on the airways is reduced. However, eventually a depth - and hence pressure - is reached at which breathing becomes too difficult regardless and this is the limit of human diving endeavours.

But free divers - who don't use any supplemental air - can go very deep, just not for very long. So if we were like whales, and adapted to hold onto a breath for hours at a time, we could dive as deep as they can. Unfortunately our biochemistry isn't up to it!