During the past few years there has been an increasing interest in applying higher‐order spectra (statistics) to a wide range of signal processing and system theory problems. These statistics are very useful in problems where either non‐Gaussianity, nonminimum phase, colored noise, or nonlinearities are important and must be accounted for. When signals are random processes, then cumulants are used as the higher‐order statistics. When they are nonrandom, then moments are used. New methods have been developed that work either in cumulant or moment domains; in their multidimensional Fourier transform (i.e., “polyspectral”) domains; or, even in inverse logarithmic (e.g., high‐order “cepstral”) domains. Applications of higher‐order spectra to acoustics problems include transient signal reconstruction based on moving average, autoregressive, or autoregressive moving average models, when measurements are colored and Gaussian; detection of transient signals (in additive colored Gaussian noise); time delay estimation when measurement noises are correlated but Gaussian; and harmonic retrieval.