Studies of "ancient DNA" are becoming all the rage these days in various circles. The term "ancient DNA" refers to DNA isolated from very old samples, lets say at least 1000 years old.
Many years ago, it was considered almost taboo among biologists to say you worked on ancient DNA. It was the cold fusion of biology. This was becuase a variety of esteemed scientists basically said it was impossible for one to study ancient DNA since DNA was not stable enough to survive for so long a period of time. It is clear now that these people were pontificating without any real evidence, but at the time, they carried a lot of weight.
At first, the papers published on ancient DNA seemed to support the naysayers. Many many early claims were found to be flawed. But as researchers learned the problems, they also learned how to circumvent them. They learned how to keep samples very clean and avoid the possibility of contamintions. And they learned how to help deal with fragile DNA (it is sort of the chemical equivalent of dealing with a crumbling manuscript of days past).
And most recently, ancient DNA has gotten a new kick in the pants. This comes from applications of methods originally designed for genome sequencing projects (like the human genome project) to the field of ancient DNA. The genome sequencing methods allow researchers to characterize in more depth samples that supposedly contain ancient DNA. The deeper sampling allows more statistical approaches to analyzing the data and this in turn allows one to test a variety of possible explanations for what one observed (e.g., one can do a test that distinguiushes contamination from other possibilities).
And one can tell that ancient DNA is really a hot topic again as it is getting covered in all sorts of popular mags (see the recent article in Wired magazine for example here).
What can one do by studying ancient DNA? Well, basically the same things that anthropologists and paleontologists and archaeologists and evolutionary biologists have been trying to do by examining fossils. Only now, by looking at the DNA contained within fossils, one can both test (i.e., confirm, deny) inferences made from other information OR one can frequently make inferences that were impossible previously (the article in Wired is about Eddy Rubin's studies of Neanderthal DNA that to them suggests that many anthropology-based claims about human-Neanderthal interbreeeding are wrong). Note - for full disclosure (which someone nagged on my previously for not doing), I am just starting to work with Eddy Rubin on some ancient DNA analyses, but I had nothing to do with the Neanderthal work described in the article.
The real question I think for ancient DNA studies is now no longer can they work. The question is - how far back can they go? Most likely, as one goes further and further back in time, the DNA will be in worse and worse shape. And thus what one can learn from looking at it will decrease significantly. But here is where the genome sequencing methods come into play. If one can get a large enough sample size, it may not matter so much that the DNA is in bad shape. For example, if one had one blurry picture of someones face, you would not know what they looked like. But if you had 10000 blurry pictures of the same face, you could reconstruct it with high accuracy by combining the information from the different pictures.
So - stay tuned - ancient DNA studies may be turning up some interesting tidbits in the near future. We are not likely to get to Jurassic Park territory soon - but it is not longer as absurd as it once seemed to many.