Canada has an impressive collection of large native mammals that everyone should feel proud about. We can boast five species of deer- the white tail, mule, elk (Wapiti), caribou, and moose. Though much reduced in range, two of Alberta's national parks are home to enormous populations of American bison. Our carnivores are no less impressive. Grizzly bears roam our western mountains, polar bears frequent the Arctic region, and black bears are found all across the country. Dogs like wolves, coyotes and foxes too make their home throughout the land, and cougars, bobcats and lynx make up our elusive wild cat population. We also have very recognizable smaller mammals, such as our emblem, the beaver, as well as small carnivores like weasels, minks, and badgers. These species all give off a distinctly Canadian feeling to those who are from here. It's interesting to learn, then, that most of the species listed here have very close relatives that are found throughout northern Eurasia. Some of these species themselves even occupy ranges that spread across the northern latitudes of both landmasses. Where does some of this overlap come from? Why can you go to Eastern Europe and run into beavers and moose? There's an answer to this: faunal interchange.
If you went back in time to the period where huge glaciation events ended up in most of North America being covered by vast sheets of ice (colloquially dubbed the "Ice Age"), you would find that the Bering Straight, the expanse of water separating the eastern tip of Russia from the western tip of Alaska, is gone. Due to the effects of glaciation, the sea levels have dramatically receded. In place of a frigid cold sea, there would be a great bridge of land joining Asia ands North America, known as Beringia. This land bridge facilitated the movement of both plants (the Boreal Forest, covering most of northern Europe, Asia and North America, has a fairly uniform set of plant species) and animals between Eurasia and North America. What species went where is a subject of interest.
Most people are surprised to learn that both camels and horses first evolved in North America. It's fairly common knowledge that all of our domestic horses here were brought over from Europe by Europeans, and small bands of wild horses still roam their native habitats on the plains of Mongolia. It's also pretty hard to picture a camel running around on the North American prairies. But they were here. When the land bridge connected them to Asia, wild horses made the trek over to the 'Old World'. Why? Possibly food. More territory perhaps. Niches for a medium-sized, galloping, grazing animal were open in Asia at the time. Either way, horses made it to Asia and spread further into Europe and Africa too, eventually going extinct in their ancestral homeland of North America. It wasn't until the Spanish brought them back during early colonization that horses once again got to see the land they (unknown to them) originated in. As for camels- the modern Dromedary and Bactrian camels, which inhabit the Middle-East and central Asia respectively, owe their ancestry to camels that followed horses on the journey from North America to Asia. Meanwhile, their relatives, the guanaco and vicuna (as well as their domestic descendants- the llama and alpaca), come from North American camels that went south into South America when the Panamanian land bridge formed.
So what did the Americas get in return for camels and horses? Well... Beavers, bears, bison, big cats, caribou, elk, foxes, humans, mammoths, mastodons, moose, wolverines, and weasels. To name a few. Yes, the ancestors of these animals which proceeded to diversify throughout North America had their start in Eurasia. These creatures traversed back and forth across Beringia and, when the land bridge vanished beneath the sea, they were trapped on both sides. The grey wolf, as well, followed a similar path from it's original home in North America, spreading widely throughout Europe and Asia. However, the level of similarity between mammals living on one side of the Pacific versus the other has some variation to it.
While beavers in the genus Castor occupy both continents, a different species is present on each landmass (canadensis in North America, fiber in Eurasia). The brown bear Ursus arctos is present on both sides, but each continent has a different collection of subspecies. The genus Bison originated in Eurasia. Although different species spread around that landmass, the only surviving one is the wisent (Bison bonasus). Upon arrival in North America, several other bison species evolved and eventually gave rise to the American bison (Bison bison) that exists to this day. Cats, such as cheetahs, lions and the famous Smilodon ranged across NA but are now extinct (however, the jaguar, a close relative of lions, tigers, and leopards manages to make a living from Mexico southwards). Moose and the relatives of todays American elk (also known as Wapiti) are present on both continents but arose in Europe. Red foxes naturally range throughout most of the Northern hemisphere and it's probable that they too came across on the land bridge (although some have argues that they were brought over by Europeans during early colonization events).
Some of the most well known animals to make it to North America were the hairy elephants- the mammoths and mastodons. Fossils of these creatures have been found from Europe to Siberia, down through Alaska and Canada and further south into the United States. As the vegetation and climate of both continents homogenized, cold-adapted elephants made the trip east across the land bridge, where they survived up until the last 10,000 years, leaving a few remarkably preserved bodies frozen into the ice of the north. It's interesting to note that, up until a certain point in time, some native people of northern Russia and Canada were trading in mammoth ivory, and believed the beasts were still alive out there somewhere. While untrue, it's a tantalizing thought.