A quasi-paradox has persisted within the field of linguistics, because the sudden emergence of such a complex, limitless system in a single species is hard to rationalize in terms of standard evolution. Its rapid spread makes language seem more like a viral epidemic that swept through the human population rather than a trait inherited through the typical dynamics of evolution.
Luckily, two recent advances have made it possible to rigorously address the problem of language's evolution for the first time. Molecular biology (including the publication of the human genome) and the so-called evo-devo paradigm now permit us to establish new and often quite unexpected connections among very different species. In addition, linguists' understanding of syntax -- how words are strung together into grammatical sentenceshas developed to the point where language can be broken down into its basic procedural components. These components can now be seen to resemble traits observed in other species -- with functions that appear to be completely unrelated to familiar thought processes. Language may indeed be unique to humans, but the processes that underlie it are not.
It hits on many of the big topics, including the comparative biology of communication in finches, the regulatory role of FoxP2 in birdsong, and the brain processes underlying syntax.
I will differ from Uriagereka on this point:
The publication of the Neanderthal genome should tell us just how different their FoxP2 gene really is from our own.
Human FoxP2 differs from chimpanzees by two derived amino acid substitutions. If Neandertals were different from us (which seems likely, given the recent evidence of selection on the gene), then they would have had only one of these substitutions. It's an answer we don't actually need the Neandertal genome for. Now, if only we could start thinking about some other language-related genes.