Frozen mice cloned; wooly mammoths on horizon
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Aside from that of course, dinosaur remains are, as far as I know, all petrified, which is somewhat worse than species that became extinct in the last couple tens of thousands of years.
The Science of Jurassic Park and the Lost World, or How to Build a Dinosaur by Rob DeSalle and David Lindley
You don't need to have read or seen Jurassic Park to appreciate the book.
At the risk of providing spoilers: The book is, ultimately, a catalog of reasons why cloning dinosaurs is impossible. ;) The simplest reason is that genetic material is very fragile, but once you get beyond that there are many more entertaining reasons, ranging from the profound (fetal development is dependent on the mother's physiology as well as the child's genetic code -- you quite literally have a chicken-and-egg problem when you're trying to clone an extinct creature) to the surprisingly profound (If a live dinosaur walked outside, could he find anything to eat, given that so many of our modern plants evolved after dinosaurs were already extinct? If he did eat anything, would he be able to digest it without his intestinal flora, many of which are probably also extinct? Or would he simply be eaten by one of our modern predators, anything from an eagle to a bacterium?)