Blue whale
No other contender for the title has a record backed by whole bodies. The longest reliably measured blue whale was a female of 33.26 meters, and a 27.1-meter female weighed at least 136.4 tons, so the longest whales would have been heavier still. The often-quoted top weight is about 190 tons.
Every fossil rival on this list is an estimate scaled up from partial bones. The blue whale's figures come from animals that were laid out, measured and weighed, and no fossil yet shows anything heavier. That is why it still holds the overall record, and why it may be the largest animal that has ever lived, not just the largest alive.
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