The neural tracking framework enables the analysis of neural responses (EEG) to continuous natural speech, e.g., a story or a podcast. This allows for objective investigation of a range of auditory and linguistic processes in the brain during natural speech perception. This approach is more ecologically valid than traditional auditory evoked responses and has great potential for both research and clinical applications. In this article, we review the neural tracking framework and highlight three prominent examples of neural tracking analyses. This includes the neural tracking of the fundamental frequency of the voice (f0), the speech envelope and linguistic features. Each of these analyses provides a unique point of view into the hierarchical stages of speech processing in the human brain. f0-tracking assesses the encoding of fine temporal information in the early stages of the auditory pathway, i.e. from the auditory periphery up to early processing in the primary auditory cortex. This fundamental processing in (mostly) subcortical stages forms the foundation of speech perception in the cortex. Envelope tracking reflects bottom-up and top-down speech-related processes in the auditory cortex, and is likely necessary but not sufficient for speech intelligibility. To study neural processes more directly related to speech intelligibility, neural tracking of linguistic features can be used. This analysis focuses on the encoding of linguistic features (e.g. word or phoneme surprisal) in the brain. Together these analyses form a multi-faceted and time-effective objective assessment of the auditory and linguistic processing of an individual.