‘Covert consciousness’ is a state in which consciousness is present without the capacity for behavioural response, and it can occur in patients with intraoperative awareness or unresponsive wakefulness syndrome. To detect and prevent this undesirable state, it is critical to develop a reliable neurobiological assessment of an individual's level of consciousness that is independent of behaviour. One such approach that shows potential is measuring surrogates of cortical communication in the brain using electroencephalography (EEG). EEG is practicable in clinical application, but involves many fundamental signal processing problems, including signal-to-noise ratio and high dimensional complexity. Symbolic analysis of EEG can mitigate these problems, improving the measurement of brain connectivity and the ability to successfully assess levels of consciousness. In this article, we review the problem of covert consciousness, basic neurobiological principles of consciousness, current methods of measuring brain connectivity and the advantages of symbolic processing, with a focus on symbolic transfer entropy (STE). Finally, we discuss recent advances and clinical applications of STE and other symbolic analyses to assess levels of consciousness.