Speech processing in the human brain is grounded in non-specific auditory processing in the general mammalian brain, but relies on human-specific adaptations for processing speech and language. For this reason, many recent neurophysiological investigations of speech processing have turned to the human brain, with an emphasis on continuous speech. Substantial progress has been made using the phenomenon of "neural speech tracking", in which neurophysiological responses time-lock to the rhythm of auditory (and other) features in continuous speech. One broad category of investigations concerns the extent to which speech tracking measures are related to speech intelligibility, which has clinical applications in addition to its scientific importance. Recent investigations have also focused on disentangling different neural processes that contribute to speech tracking. The two lines of research are closely related, since processing stages throughout auditory cortex contribute to speech comprehension, in addition to subcortical processing and higher order and attentional processes.