The Eocene epoch, which we leave behind, saw super-greenhouse conditions, and tropical forests extending to high latitudes. The Oligocene, starting 34 million years ago, sees a drop in atmospheric CO2 levels. Glaciers begin forming in Antarctica, and the world cools sharply. There are extinctions in a number of groups (although not on the scale of the Big Five mass extinctions), after which the fauna, at least in Eurasia/North America, starts looking like what we’re used to: versions of horses, deer, camels, elephants, cats, dogs, and many rodent families begin to dominate.
The Oligocene also boasts also the largest land mammal of all time, Indricotherium (or Baluchitherium, discovered 1922), related to living rhinoceroses, but 15 feet high at the shoulders, and weighing as much as three or four African elephants. (The picture below compares them.) Indricotherium was big enough to browse high up on trees. By contrast, living big browsers (giraffes, elephants) use special bits of anatomy (long necks, trunks) to reach that high, and don’t get quite as big.
This is still a lot smaller than the biggest dinosaurs, the sauropods. Ginormousness is one of the things dinosaurs are famous for, even though there were plenty of small dinosaurs too. Two things that keep mammals from getting truly huge are probably (1) a different respiratory system, without the extensive airsacs and aerated bones of dinosaurs, and (2) live birth. Gigantic sauropods could lay eggs and produce (relatively) small offspring which grew up quickly, so they didn’t pay as high a reproductive penalty for being big.
There are other possibilities. Jose Canseco, former Major League Baseball player, and authority on being large (he is the author of Juiced: Wild Times, Rampant ‘Roids, Smash Hits, and How Baseball Got Big), published his theory on Twitter in 2013 (February 17-18). “My theory is the core of the planet shifted when [a] single continent formed to keep us in a balanced spin. The land was farther away from the core and had much less gravity so bigness could develop and dominate.” Anticipating possible criticism, he tweeted, “I may not be 100% right but think about it. How else could 30 foot leather birds fly?”