Modern spectrally efficient optical communication systems utilize polarization-multiplexed coherent transmission in complex modulation format. Coherent receivers used in these systems measure the amplitude and phase of the optical signals for both orthogonally polarized components carrying information. Knowledge of the amplitude and phase of the optical field, in combination with digital signal processing, gives the receiver an inherent metrology and performance monitoring capability. As the optical signal propagates from the transmitter over optical fiber to the receiver, a signal transformation and degradation is expected. The receiver observes the properties of the transmitted optical signal as degraded by the impairments of the transmission medium. The details of monitoring optical signal parameters and link impairments are the focus of this paper. The optical signal parameters include polarization state and residual carrier phase; optical link impairments include chromatic dispersion and polarization mode dispersion. Two distinct techniques are presented: one based on Stokes space analysis, and the other on Kalman filtering. The Stokes space techniques are modulation-format independent and do not require demodulation. The Kalman filtering provides optimal estimation of the physical quantities that describe the optical signal and the optical medium.