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Statistical signal processing has been one of the key technologies in the development of wireless communication systems, especially for broadband multiuser communication systems which severely suffer from intersymbol interference (ISI) and multiple access interference (MAI). This article reviews batch processing algorithms for blind equalization using higher-order statistics for mitigation of the ISI induced by single-input, single-output channels as well as of both the ISI and MAI induced by multiple-input, multiple-output channels. In particular, this article reviews the typical inverse filter criteria (IFC) based algorithm, super-exponential algorithm, and constant modulus algorithm along with their relations, performance, and improvements. Several advanced applications of these algorithms are illustrated, including blind channel estimation, simultaneous estimation of multiple time delays, signal-to-noise ratio (SNR) boost by blind maximum ratio combining, blind beamforming for source separation in multipath, and multiuser detection for direct sequence/code division multiple access (DS/CDMA) systems in multipath.