A Costas loop is a phase-locked loop used for carrier phase recovery from suppressed-carrier modulation signals, such as from double-sideband suppressed carrier signals. It was invented by John P. Costas at General Electric in the 1950s. Its invention was described as having had "a profound effect on modern digital communications". The primary application of Costas loops is in wireless receivers. Its advantage over the PLL-based detectors is that at small deviations the Costas loop error voltage is sin(2(θi−θf)) vs sin(θi−θf). This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking doppler-shifted carriers esp. in OFDM and GPS receivers 
In the usual implementation of a Costas loop, a local voltage-controlled oscillator provides quadrature outputs, one to each of two phase detectors, e.g., product detectors. The same phase of the input signal is also applied to both phase detectors and the output of each phase detector is passed through a low-pass filter. The outputs of these low-pass filters are inputs to another phase detector, the output of which passes through noise-reduction filter before being used to control the voltage-controlled oscillator. The overall loop response is controlled by the two individual low-pass filters that precede the third phase detector while the third low-pass filter serves a trivial role in terms of gain and phase margin.
^ D. Taylor (August 2002). "Introduction to `Synchronous Communications', A Classic Paper by John P. Costas". Proceedings of the IEEE 90 (8): pp. 1459–1460.