Placental mammals, infraclass Eutheria (meaning "true/good beast" in Greek) are the dominant group within mammals in general (a classification which also includes marsupials and monotremes), and the dominant group of terrestrial vertebrates. This has been the case since the extinction of the non-avian dinosaurs 65.5 million years ago. Although placental mammals consist of fewer species (about 4,900 total) than reptiles (8,200 species), amphibians (6,100 species), or birds (10,000 species), placental mammals are dominant in that they are the most numerous, occupy the most niches, are the largest, and a placental mammal almost always occupies the highest positions in the terrestrial food chain, Australia being the primary counterexample.
Placental mammals consist of 20 orders contained within four superorders: Xenarthra (an early placental mammal breakaway family includes armadillos, sloths, and anteaters); Laurasiatheria (including the bulk of mammal species), Afrotheria (smaller group of Africa-originating animals including tenrecs, aardvarks, hyraxes, golden moles, elephant shrews, elephants and manatees); and Euarchontoglires (a sister group of Laurasiatheria that includes rabbits, hares, rodents, primates, treeshrews, and colugos). These superorder arrangements are based on varying levels of support from molecular genetics and fossil evidence, though some are quite controversy, substantially contradicting earlier classifications based on morphology.
The four largest orders of placental mammals are Chiroptera (bats), Rodentia (mice, rats), Carnivora (dogs, cats, bears, other placental carnivores), and Cetartiodactyla (all even-toed ungulates, like pigs and buffalo, and cetaceans, which includes whales and dolphins). Despite large numbers of species, gross morphological variation is somewhat limited in the first two orders, but large in the second two. It is hard to imagine that pigs and goats are part of the same order as whales and dolphins, but it's true. These groups split apart about 60 million years ago, during the first major waves of placental mammal diversification.
Today, the majority of all placental mammals, on an individual-count basis, are human beings, our pets, livestock, and animals adapted to living close to us, especially rats and mice. In our short, 200,000 year period on the world stage, humans have radically reshaped the picture of placental mammal biodiversity. Hundreds if not thousands of placental mammals went extinct when humans spread across the world, bringing with them hunting tools like spears and axes, something that the wholly biological world could not adapt fast enough to defend against. As a result, many of the impressive placental mammal megafauna of old, like saber-tooth cats and mammoths, are now completely extinct. Numerous placental mammals continue to go extinct due to habitat destruction and other factors.