It's well known that modern baleen whales are the heaviest animals of all time, with the blue whale outclassing the largest dinosaurs in terms of weight though maybe not in terms of length. While they have a well-known reputation for gentility, all of them are carnivorous. They feed by gulping down huge masses of small animals, filtering out the water via their baleen plates. Even within this group there are different feeding styles.
The streamlined rorqual whales are active feeders, and sometimes pursue large schools of fish. Right whales are far more passive, feeding by merely sifting out small planktonic animals from the water while swimming along the surface. They do not use power, speed and lunge feeding to capture their prey.
Baleen whales may be huge now but they started out tiny. They were hardly bigger than small dolphins and porpoises at one time. These were the so-called "archaeomysticetes". This is a rather loose grouping of animals that emerged somewhere during the Priabonian Stage of the Late Eocene, roughly 38 to 33 million years ago. They evolved from the earlier archaeocetes. The later archaeocete whales, members of the Basilosauridae, were the first to truly exploit the oceans. Some of them retained the peg-like teeth in their toothed descendents.