This article lays out the case against Chomsky’s universal grammar theories. Essentially, despite decades of refining the theory, it has never been able to accommodate all languages. More damningly, it doesn’t correspond to research about how children learn their native language.
The alternatives that are coming up, it seems, view language a bit like the way neuro-scientists are starting to think about consciousness, as an emergent property of the brain. The authors are careful to denote that there is no comprehensive, widely-accepted usage theory to replace universal grammar. But, as more and more corpora become available and more brain science is done, it is very likely that a better model will emerge.