Paleocene

The Palaeocene or Paleocene ("Old New", from Greek palaios, "older", kainos "new") is the first epoch of the Paleogene period of the modern Cenozoic era. The Palaeocene starts with the K-Pg extinction event which wiped out the Non-avian dinosaurs and ended with the Palaeocene-Eocene Thermal Maximum, which resulted in a mass extinction of deep-sea algae and a major turnover of mammals on land around 55.8 Mya. The Palaeocene starts around 66-65 Mya to 56-54 Mya (according to different sources, it ended 56 according to some sources, 54 according to others).

The Earth's continents during the Paleocene were approaching their modern positions. Laurasia had split into North America, Europe, and Asia. Down south things were a bit less familiar. India was still an island and South America, Australia, and Antarctica were still slightly connected. Climate-wise, everything was warmer than it is today. Even Antarctica was tropical. Though that would start to change in the Oligocene.

The K-Pg Extinction Event ended up with new ecological niches vacant, which resulted in an explosive evolutionary radiation of mammals, birds, snakes, fish and crocodiles, with many new bird orders and families appearing. The earliest owls appeared in France and North America during the Late Palaeocene.

Paleoclimatology of the Paleocene
The Paleocene epoch preceded the Paleocene-Eocene Thermal Maximum, which was the most rapid warming event in earth's "recent" geological history, and so while the climate of the Paleocene was warmer than it is today, it was nowhere near as tropical and humid as the following Early Eocene epoch, which succeeded the Paleocene-Eocene Thermal Maximum. In general the climate of the Paleocene was relatively humid, warmer than it is now, with the poles being relatively cool and temperate. It was a time when crocodiles swam off of the coast of Patagonia and Greenland, and a time when tropical evergreens flourished as far north as Alaska.

Late-surviving dinosaurs?
Some people like to claim that some dinosaurs survived the end-Cretaceous extinction event, using a femur of a hadrosaur found in Paleocene deposits, dated roughly to 64.2 Ma, as evidence to support this postulation, but it is more likely that the hadrosaur fossil is simply a case of reworking. Reworking occurs when water cuts into old sediments, mixing up old sediments with new sediments, and heretofore jumbling together all the remains found in those sediments. While it is indeed possible that some non-avian dinosaurs survived the K-Pg extinction event, the evidence for survival is weak, and the probability therefore remains low.