Optical communications is undergoing a digital revolution, as digital signal processing (DSP) emerges as a practical
solution for robust long-haul transmission. In contrast to previous systems, in which optical dispersion compensation
was considered a necessity, recently uncompensated long-haul transmission has been demonstrated using DSP at the
transmitter, receiver, or a combination of the two. We review the historic developments of electronic signal processing
as applied to optical communications before focusing the latest developments, namely digital coherent systems. We then
discuss the salient features of the electronic signal processing schemes currently under investigation before discussing
the challenges and opportunities offered by electronic signal processing.