The performance of coherent optical receivers is affected by the phase noise of the laser transmitter and the laser local oscillator and by the shot noise due to the detectors employed in the receiver. In this paper, the performance of coherent optical receivers is discussed, taking into account both noise sources. Further, the maximum permissible laser linewidth AP for coherent optical communications systems is reported. Both heterodyne and homodyne systems are considered. It is shown that the value of AP depends on the system bit rate Rb and on the modulation/demodulation technique employed: for heterodyne receivers with noncoherent postdetection processing [used in conjunction with amplitude-shift keying (ASK) or frequency-shift keying (FSK) modulation formats], Av_0.09 Rb; for heterodyne receivers with coherent postdetection processing [used in conjunction with the phase-shift keying (PSK) modulation format], Av< 2.26 X 10-3 Rb; and for PSK homodyne receivers, Av 3.1 X 10-4Rb. This paper presents the main results only; details of the mathematics involved have been published elsewhere. The purpose is to give a user a set of simple laser linewidth requirements without forcing him to analyze the research results scattered among several publications.