Faraday isolators play a key role in the operation of large-scale gravitational-wave detectors. Second-generation gravitational-wave interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo will use high-average-power cw lasers (up to 200 W) requiring specially designed Faraday isolators that are immune to the effects resulting from the laser beam absorption-degraded isolation ratio, thermal lensing, and thermally induced beam steering. In this paper, we present a comprehensive study of Faraday isolators designed specifically for high-performance operation in high-power gravitational-wave interferometers.