A positive displacement rotary compressor is designed for near isothermal compression, high pressure ratios, high revolutions per minute, high efficiency, mixed gas/liquid compression, a low temperature increase, a low outlet temperature, and/or a high outlet pressure. Liquid injectors provide cooling liquid that cools the working fluid and improves the efficiency of the compressor. A gate moves within the compression chamber to either make contact with or be proximate to the rotor as it turns.