We present a method for visualizing single-trial evoked potentials and show applications of the consequent single-trial analysis. The method is based on the wavelet transform, which has an excellent resolution both in the time and frequency domains. Its use provides new information that is not accessible from the conventional analysis of peak amplitudes and latencies of average evoked potentials. We review some of the applications of the single trial analysis to the study of different cognitive processes. First, we describe systematic trial-to- trial changes reflecting habituation and sensitization processes. Second, we show how an analysis of trial-to-trial latency variability gives new insights on the mechanisms eliciting a larger mismatch negativity in control subjects, in comparison to sleep deprived subjects when performing a pattern recognition learning task. Third, we show in a rhythm perception task that trained musicians had lower latency jitters than non-musicians, in spite of the fact that there were no differences in the average responses. We conclude that the single trial analysis of evoked potentials opens a wide range of new possibilities for the study of cognitive processes.