Following the loss of wakeful consciousness, the averaging of responses to stimuli produce evoked potential waveforms with prominent components either unique to or greatly enhanced by non-REM sleep. In the sleep onset periods (stage 1) these are the P2 and N350. Following the establishment of stable sleep (stage 2 and SWS), the N550 and P900 are also prominent. Investigation of the EEG associated with individual responses indicates that a good proportion of stimuli elicit, K-complexes or vertex sharp waves (VSWs) and occasionally will elicit both. Recent work has indicated that the N550 in the averaged response is due to the presence of K-complexes and that the N350 is at least largely due to the presence of VSWs. The large size of these grapho-elements indicates that they are probably produced by a synchronized discharge of multiple neural units. Both are readily observed in the absence of external stimulation and occur as normal components of sleep, indeed the K-complex is used as one of the identifying features of the onset of stable non-REM sleep. The present review details the investigation of these features and their associated evoked potential components, in terms of stimulus features, brain states associated with their production, their scalp topography, and changes as a function of age.