Auditory training is evidenced by a change in a listener's ability to perform an auditory perceptual task. The result of training - auditory learning - can occur very rapidly from a wide range of training scenarios. Scientific auditory training has the potential to revolutionize professional practice by providing highly efficient and quantitatively verifiable tools for the management of a range of listening/language impairments including auditory processing disorder, specific language and reading impairment, and sensorineural and conductive hearing loss. Our research has focused on discovering the rules of auditory learning and implementing those rules into useful applications. Surprising results have emerged on both fronts. Although training tasks may be too easy to produce optimal learning, the opposite is not true; we have shown robust learning on an impossibly difficult task, thereby emphasizing the importance of active engagement with the task. However, listening to sounds need not be a necessary component of the training - playing a visual spatial task (the computer game Tetris) led to improved performance on an auditory task. For language learning, several studies have found that auditory training using simple sounds can produce wide-ranging improvements in receptive language skills and literacy. Auditory learning includes enhancement of both top-down cognitive processing and bottom-up sensory processing. The most important outstanding issue is further understanding of the transfer of training - the relation between what is trained and what is learned.