Blue whales and other filter-feeding leviathans became giants when climate change introduced them to binge-eating, research has shown.
At more than 100ft long, the blue whale is the largest vertebrate animal that has ever lived.
It also dwarfs its ancestors. Scientists have discovered that whales with bodies longer than 10 metres only made an appearance roughly 4.5 million years ago.
We live in a time of giants. Baleen whales have never been this big, ever.
At the same time, smaller species of whale began to vanish, suggesting that large size was suddenly an important advantage.
The reason for the size expansion of the blue whale and other baleen whales was food, the researchers believe.
All baleen whales have a filter system in their mouth that sifts out tiny shrimp-like sea creatures known as krill.
As ice sheets covered the northern hemisphere, krill ceased to be distributed thinly throughout the oceans.
Instead, it became concentrated at certain times of year in coastal areas where run-off from the newly formed ice caps washed nutrients into the sea.
For the whales, it made sense to make the most of the seasonal abundant food by bingeing. Filter-feeding and large body size both made for more efficient eating when faced with dense accumulations of prey.
A member of the US team from the University of Chicago, Dr Graham Slater, said: "We might imagine that whales just gradually got bigger over time, as if by chance, and perhaps that could explain how these whales became so massive.
"But our analyses show that this idea doesn't hold up - the only way that you can explain baleen whales becoming the giants they are today is if something changed in the recent past that created an incentive to be a giant and made it disadvantageous to be small."
The scientists analysed fossil whale skulls housed at the Smithsonian Institution's National Museum of Natural History in Washington DC to estimate the size of 63 extinct species.
Among the fossils were the earliest baleen whales, which lived more than 30 million years ago.
The team incorporated data from 13 species of modern whale to work out evolutionary relationships between whales of different sizes.
The findings, published in the journal Proceedings of the Royal Society B, clearly showed that for most of their history, baleen whales were nothing like as large as they are today.
Co-author from Stanford University in California, Dr Jeremy Goldbogen, said: "We live in a time of giants. Baleen whales have never been this big, ever."
Another advantage of large size was the ability to make epic journeys of thousands of miles to take advantage of seasonally abundant food supplies, said the scientists.
Curator of fossil marine mammals at the Smithsonian museum, Dr Nicholas Pyenson, said: "Our research sheds light on why today's oceans and climate can support Earth's most massive vertebrates.
"But today's oceans and climate are changing at geological scales in the course of human lifetimes.
"With these rapid changes, does the ocean have the capacity to sustain several billion people and the world's largest whales?
"The clues to answer this question lie in our ability to learn from Earth's deep past - the crucible of our present world - embedded in the fossil record."