The oldest and most primitive cats are called nimravids. They are very primitive carnivores and there is disagreement as to whether or not they should be classified as members of Feliformia or Caniformia.  In either case, they are not closely related to modern cats and they became extinct without leaving any living descendants.  Just as in the true felid cats, they varied in size and a variety of species evolved with enlarged canines (Bryant, 1991).  The primitive Eofelis is closest to the origin of nimravids (Peigne, 2001).
skulls nimravid eusmilus
nimravis barbourofelis
Felid cats have varied greatly in size, even within the same genus such as the cougar and domestic cat pictured below (genus Felis).
cougar sabertooth
saber bite
    The earliest true felid was Proailurus from Early Miocene.  The early fossil cat Pseudaelurus still had 5 toes.  The scimitar-toothed cat Homotherium preyed on young mammoths and could drag their carcasses to caves where they made their dens. Their front legs were elongated. A number of species evolved enormous canines that could have been used on the throats of victims as seem below.
felid skull felid skull 2 felid skull 3
felid skull 4 smilodon skeleton
While a number of cats evolved large canines, the genus Smilodon possessed the largest canines.

Genetic analysis suggests that the diversification of modern cats began in the Late Miocene. Prior to the Late Miocene, the carnivore relatives of cats (hyaneas, mongoose, civets, and genets) had diverged. The first modern cat lineage to separate from that of the others is that of the genus Panthera: lions, jaguars, tigers, and leopards. After that, a number of cat lineages evolved in succession: the bay cat lineage (bay cats, marbled cats, and Asian golden cats), caracals (caracals, African golden cats, servals), the ocelot lineage (ocelot, margay, Andean mountain cat, pampas cat, geoffrey’s cat, kodjods, and tigrinas), the lynx lineage (lynxes and the bobcat), the puma lineage (puma, jaguarandi, and cheetahs), leopard cats (pallas cat, rusty spotted cat, Asian leopard cat, fishing cat, and flat-headed cat), and the domestic cat lineage (domestic cat, European wild cat, African wild cat, Chinese desert cat, desert cat, black footed cat, and jungle cat) (Johnson, 2006).

Three million years ago, North America’s cats included the giant cheetah Miracinonyx (which had a similarly sized European relative), the lion-sized saber-toothed cat Ischyrosmilus, and the slightly smaller Megantereon hersperus which was ancestral to the largest saber-toothed cat, Smilodon (Kurten, 1988). Fossil Cats include a fossil cheetah, Miracinonyx which was larger than modern cheetahs and lived in North America, an American lion, Panthera atrox, and the European jaguar which was larger than the modern jaguar (Panthera gombaszoegensis).Jaguars evolved in Eurasia and migrated to North America about 1.9 million years ago. The first jaguars in North America were similar to lions in their size and body proportions but gradually became smaller and stockier as they adapted to more wooded environments (Kurten, 1988). The first lions are known from Africa from about 2 million years ago. One species traveled to Europe about 700,000 years ago and it was the largest species of lion although its brain was comparatively small. From there it migrated to Asia, then to North America and even to South America (as far south as Peru) (Kurten, 1988).

cats fossil cheetah