It now looks like mammals branched out a little 65 million years ago, but waited another 10-15 million years to really diversify.
Science assumed that mammals evolved as soon as dinosaurs perished. This was based on the facts that mammals did branch out after the dinosaurs perished, and dinosaurs weren't around to stop the mammals from evolving. However, evolution usually only happens when it is needed to happen, so that species can increase their chance of survival.
What we do know is no animal larger than a house cat survived very long past the meteorite hit, or hits of around 65 million years ago. We do know that oxygen levels on earth were much higher than they are now, as well.
A large meteorite hit would most likely cut off sunlight (which is a big part of current theory), and most of the plant life on the planet died.
All that were left on land, were small detritivores (cool, I learned a new word). Food was a plenty for these animals, which included insects and little rodent like mammals.
When food is plentiful, and the environment stays somewhat stable, there is no need to evolve. Also, because the larger animals perished, what most likely happened is that large plants and trees died, causing large herbivores to die, causing large carnivores to have nothing to eat. They couldn't survive on the smaller animals who already knew how to hide from the big guys, more or less.
I don't think loss of trees and large plants was all there was to the dinosaurs demise, because they weren't quite cold blooded reptiles, and many small reptiles did survive. Studies have shown their body temperatures varied with size.
Body temperature and the abrupt change in oxygen content most likely was the greatest contributor to dinosaur extinction, but science doesn't know for sure YET. The jury is still out to why small dinosaurs also perished, or did they evolve into birds after the meteorite hit, or something else that went extinct?
Not knowing YET doesn't mean that God exists. And it definitely doesn't mean that because science doesn't know YET, that the earth is less than 10,000 years old and evolution didn't happen.
There is a good chance that the atmosphere slowly changed, or maybe abruptly changed around 50 million years ago, causing plants to get bigger and trees to grow again, which led to different food sources and a need for some animals to get bigger to have a greater chance of species survival.
Many headlines for the above story make it seem that the dinosaur's demise had no bearing on allowing mammals to evolve. The thing they are missing is that without the dinosaur's extinction, mammals would most likely never have got bigger than a small cat, or they would have been easy targets for snacking.
If the meteorite missed, dinosaurs would most likely be still dominating the planet, and only small mammals might still be here. Except for the free-range large mammals, the now highly intelligent dinosaurs bred on farms, for food.
I added these tectonics maps showing continental drift at three crucial times. Remember, placental mammals and marsupial mammals branched out around 110 million years ago. Placental mammals didn't make it to Australia for quite some time after the big asteroid hit.
Isolation of the marsupial mammals, coupled with plenty of food and shelter, probably had something to do with the fact that no Aussie animal developed their intelligence into anything that resembled man or bonobo or dolphin. Maybe next meteorite crash, the Australian little rodents that survive, will be the ones that lead to the most intelligent species on the planet, eventually.
For real science from real scientists on this topic, check out Sandwalk and Pharyngula.