This talk presents techniques for nonstationarity detection in the context of speech and audio waveforms, with broad application to any class of time series that exhibits locally stationary behavior. Many such waveforms, in particular information-carrying natural sound signals, exhibit a degree of controlled nonstationarity, and are often well modeled as slowly time-varying systems. The talk first describes the basic concepts of such systems and their analysis via local Fourier methods. Parametric approaches appropriate for speech are then introduced by way of time-varying autoregressive models, along with nonparametric approaches based on variation of time-localized estimates of the power spectral density of an observed random process, along with an efficient offline bootstrap procedure based on the Wold representation. Several real-world examples are given.