Publisher Summary This chapter reviews the theory of multilevel modulation formats that permit multiple bits/s of data per Hz of bandwidth and evaluates the results of recent developments on the digital coherent receiver. The fundamental concept behind coherent detection is to take the product of electric fields of the modulated signal light and the continuous-wave local oscillator (LO). Outputs from the homodyne phase/polarization diversity receiver are processed by digital signal processing (DSP) circuits, restoring the complex amplitude of the signal in a stable manner despite of fluctuations of the carrier phase. Hereafter, such receiver is called the digital coherent receiver. The chapter investigates the digital coherent receiver where the carrier phase is estimated with DSP, alleviating locking the phase of the LO to the carrier phase in the conventional homodyne receiver. It has been found that the phase noise of state-of-the-art semiconductor distributed feedback (DFB) lasers is substantially small such that an accurate phase estimate can be obtained from the sampled signal to demodulate M-ary PSK signals up to eight phase states at the symbol rate of 10 Gsymbol/s.