NHM: Predator and Prey?
This is Smilodon, a sabre-tooth cat.
Their prey were mostly large herbivores: bison, horses, and the extinct ground sloths and mastodons (amongst many others). Their limbs and "upper body" are much more massive than those of extant large cats, and it is thought that they would ambush their prey, wrestle them to the ground, and then deliver a lethal bite to the throat with their long canines stabbing through and cutting the jugular veins and trachea causing a quick death.
Unfortunately, they went extinct about 10,000 years ago in part of the (still-occurring) Holocene mass extinction in which many of the largest land mammals (including mammoths, glyptodonts, giant sloths, and the largest species of many other taxa) died out. There is still no consensus on whether these megafaunal extinctions constitute part of the Quaternary extinction event (caused, perhaps, by human overkill, the extinction of mammoths and subsequent habitat and climate changes, or natural climate change associated with the Ice Ages), or whether they are result of human-induced habitat and climate changes. It is sad to see any species go extinct and we no doubt suffer as a species for the loss of diversity across the world, but, on the other hand, these apex predators would have had no qualms about snatching a pink-coated child (say), so I'm sure that parents the world over are glad that all that remains are skeletons...