N onstationarity relates to the variation over time of the statistics of a signal. Therefore, signals from practical applications that are realizations of nonstationary processes are difficult to represent and to process. In this article, we provide a comprehensive discussion of the asynchronous representation and processing of nonstationary signals using a time-frequency framework. Power consumption and type of processing imposed by the size of the devices in many applications motivate the use of asynchronous, rather than conventional synchronous, approaches. This leads to the consideration of nonuniform, signal-dependent level-crossing (LC) and asynchronous sigma delta modulator (ASDM)-based sampling. Reconstruction from