Assessing adequacy of anesthesia requires evaluation of its components: hypnosis, analgesia, and neuromuscular transmission. In order to do this, many methods have been developed that process signals representing different modalities. Assessment of hypnosis requires cortical measures of the central nervous system (CNS); methods that assess analgesia concentrate on subcortical and spinal levels of the CNS; and neuromuscular transmission is a peripheral phenomenon. This article presents an overview of the current state of methods available for measuring each of these components. We conclude that, whereas important gains have been made in the area of assessment of hypnosis, mainly owing to the advancement of methods using EEG and auditory evoked potentials, and whereas neuromuscular transmission can be objectively monitored using motor nerve stimulation, assessment of analgesia still contains many challenges.