More Information on Neanderthals: http://humanorigins.si.edu/evidence/human-fossils/species/homo-neanderthalensis
DNA is a very fragile molecule, and it tends to break down quickly over time. As a result, it can often be difficult, or even impossible, to find DNA of organisms that lived millions of years ago. However, scientists have recently discovered a new method to obtain DNA samples from Neanderthals, even without any fossils. They did this by collecting samples of cave sediments and searching them for mitochondrial DNA. They were able to find the DNA of multiple species, one of which was Neanderthals.
This discovery has me very excited to find out what new information we will learn about ancient species. I'm also curious as to how far back this method can retrieve DNA. While I doubt that it will go back much further, due to the fragile nature of DNA, it is still exciting.