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Digital signal processing (DSP) combined with coherent detection has played a central role in the recent capacity expansion of optical networks. Optical superchannels aim to increase per-channel interface rates as well as per-fiber capacities of wavelength-division multiplexed (WDM) systems in a cost-effective manner. Superchannels circumvent the electronic bottleneck via optical parallelism and provide high-per-channel data rates and better spectral utilization, especially in transparent optical mesh networks. This article reviews recent advances in the generation, detection, and transmission of optical superchannels with channel data rates on the order of terabits per second (Tb/s). Enabling DSP techniques such as Nyquist-WDM, orthogonal frequency-division multiplexing (OFDM), software-defined modulation and detection, advanced coding, and joint DSP among the superchannel constituents are presented. Future prospects of DSP techniques for high-capacity superchannel transmission are also discussed.