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A definitive goal for optical performance monitoring in an optical communications network is to provide comprehensive signal quality information in a cost-effective manner. This paper explores in detail the possibility of using nonlinear optical detection to achieve this goal. Sensitive nonlinear detection techniques commonly used in the field of ultrafast optics are applied to the problem of performance monitoring and are shown to allow quantitative measurements to be made of quantities such as accumulated chromatic dispersion, polarization-mode dispersion impairment, optical signal-to-noise ratio, and extinction ratio. Experiments performed on a 40-Gb/s transmission system demonstrate the immediate viability of this approach for measuring these quantities of interest at practical optical power levels.