This paper is aimed at presenting the two main classes of nonstationary signal transforms that are currently used to analyze and to characterize EEG observations. Time-scale methods, or wavelet transforms, allow a time versus duration analysis to be performed whereas time-frequency methods allow spectral contents to be analyzed as a function of time. These two types of transform are well suited to the study of changes either localized or progressive that may be observed in EEG signal dynamics and that sign the evolution of underlying physiological mechanisms. The potential interest of these methods in nonstationary signal representation is illustrated through several academic examples. Then, methods are applied on real EEG signals to solve problems such that the detection of interictal transient signals (like spikes or spike-waves) and the recognition of signatures during ictal periods.