Auditory streaming refers to the perceptual parsing of acoustic sequences into "streams", which makes it possible for a listener to follow the sounds from a given source amidst other sounds. Streaming is currently regarded as an important function of the auditory system in both humans and animals, crucial for survival in environments that typically contain multiple sound sources. This article reviews recent findings concerning the possible neural mechanisms behind this perceptual phenomenon at the level of the auditory cortex. The first part is devoted to intra-cortical recordings, which provide insight into the neural "micromechanisms" of auditory streaming in the primary auditory cortex (A1). In the second part, recent results obtained using functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) in humans, which suggest a contribution from cortical areas other than A1, are presented. Overall, the findings concur to demonstrate that many important features of sequential streaming can be explained relatively simply based on neural responses in the auditory cortex.