The prospects for using fiber optical parametric amplifiers (OPAs) in optical communication systems are reviewed. Phase-insensitive amplifiers (PIAs) and phase-sensitive amplifiers (PSAs) are considered. Low-penalty amplification at/or near 1 Tb/s has been achieved, for both wavelength- and time-division multiplexed formats. High-quality mid-span spectral inversion has been demonstrated at 0.64 Tb/s, avoiding electronic dispersion compensation. All-optical amplitude regeneration of amplitude-modulated signals has been performed, while PSAs have been used to demonstrate phase regeneration of phase-modulated signals. A PSA with 1.1-dB noise figure has been demonstrated, and preliminary wavelength-division multiplexing experiments have been performed with PSAs. 512 Gb/s have been transmitted over 6,000 km by periodic phase conjugation. Simulations indicate that PIAs could reach data rate x reach products in excess of 14,000 Tb/s × km in realistic wavelength-division multiplexed long-haul networks. Technical challenges remaining to be addressed in order for fiber OPAs to become useful for long-haul communication networks are discussed.