Humans and animals must often discriminate between complex natural sounds in the presence of competing sounds in the background, a problem often referred to as the "Cocktail Party Problem". This problem has been difficult to solve using engineering or machine learning approaches. The fact that normal hearing listeners can solve it suggests the existence of a solution in the brain.The auditory cortex is thought to be important in solving this problem. I will discuss a series of experiments in the auditory cortex analog in the songbird which reveal cortical interference effects that may lie at the heart of the problem, and point to a biologically plausible strategy for solving it.