This vast period of time (right after the extinction of non-avian dinosaurs and other major mesozoic life) included about 42 million years, consisting of the Paleogene, Eocene, and Oligocene Epochs. Many changes occurred in the positions of continents, climates, and huge biodiversity turnover.
The longest & perhaps most important period was the Eocene (~56-34 MA), in which many modern animal groups arose, both on land and in aquatic niches. Even species related to modern ones looked exotic (by modern standards).
Significant/ Noteworthy Events:
Paleocene (65-56 MA):
-Plankton diversity recovers (Diatoms & dinoflagellates less affected than coccolithopores, diatoms steadily become more diverse over time)
-Radiation of mammals & other terrestrial animals (including the largest snake ever, mammals become overall larger & more dominant, large flightless birds, etc.)
-Lamniform shark diversity rebounds (had serious competition in the late Cretaceous with mosasaurs, plesiosaurs, & large bony fish)
Over 2 inch Palaeocarcharodon tooth
-Global warming persists into the early Eocene
Eocene (56-34 MA):
-Significant global warming/ hotbox earth in early Eocene (massive radiations of life in invertebrates & vertebrates; no glaciers at poles nor cold deep ocean water)
-Radiation of perciform fishes (& a lot of other modern fish groups), first Carcharhiniform sharks that resemble predatory lamniform sharks (previously only small catsharks) and appearances of most modern mammal orders
-Evolution of whales and sirenians (dugongs & later manatees) from terrestrial ancestors
Predatory Archarocete whale skulll (Zygorhiza). Closely related Basilosaurus was the top predator of the Marine Late Eocene & grew up to perhaps 50- 60 feet.
-Large Mid Eocene extinction (perhaps even more devastating than the Late Eocene- Early Oligocene exitinctions; both linked to climate change)
-Climate fluctuates but overall much cooler into start of Oligocene
Oligocene (34-23 MA):
-Global cooling/ glaciation in early Oligocene
-Extinction of first fully aquatic whales (Archaocetes), rise of modern whale orders (Baleen and Modern Toothed whales)
-Diversification of Carcharhiniform sharks (now as prevalent/ divserse as lamniform sharks, if not more)
Oligocene toothed whale & dolphins
Source: Prothero's "After the Dinosaurs" book