The investigation into neural basis of speech processing, including distributed hierarchical organization, neural mechanisms, and functional connectivity of brain, stands in the central of neurolinguistic research. In line with the sequence of speech processing, it can be subdivided into three processing stages: spectrotemporal analysis of primary acoustic signals, phonemic processing, and lexical-semantic processing. Despite underlying neural mechanisms of these stages have been investigated extensively and intensively, it appears that there are still inconsistencies and controversies between different model theories/hypotheses. Consequently, it is crucial to sort out and summarize them. The present review takes the three speech processing stages of the brain as the main line and reviews the research status of neurological mechanism under each stage, covers cortical mapping, neural oscillations, and event-related potential characteristics. Of note, this review focuses more on observations based on the electrophysiological approaches. We aiming to synthesize the latest findings of this field and provide new insights for understanding how speech signals are represented and processed in the human brain.