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The performance and complexity of signal processing systems for underwater acoustic communications has dramatically increased over the last two decades. With its origins in noncoherent modulation and detection for communication at rates under 100 b/s, phase-coherent digital communication systems employing multichannel adaptive equalization with explicit symbol-timing and phase tracking are being deployed in commercial and military systems, enabling rates in excess of 10 kb/s. Research systems have been shown to further dramatically increase performance through the use of spatial multiplexing. Iterative equalization and decoding has also proven to be an enabling technology for dramatically enhancing the robustness of such systems. This article provides a brief overview of signal processing methods and advances in underwater acoustic communications, discussing both single carrier and emerging multicarrier methods, along with iterative decoding and spatial multiplexing methods.