Recent progress in coherent optical communication, a field revived by advancesin digital signal processing (DSP), is reviewed. DSP-based phase andpolarization management techniques make coherent detection robust andpractical. With coherent detection, the complex field of the received signal isfully recovered, allowing compensation of linear impairments includingchromatic dispersion and polarization-mode dispersion using digital filters. Inaddition, fiber nonlinearities can also be compensated by using backwardpropagation in the digital domain.