This chapter describes some displacement compressors including roots compressor, vane compressor, screw compressor, mono-screw compressor, scroll compressor, tooth rotor compressor, and liquid ring compressor. Most compressors described are used in air-conditioning and refrigeration applications. The operation principle of the roots compressor is essentially different from that of the piston compressor because there is no internal compression and there are no valves. Like a roots compressor the vanes compressor has no valves but ports. But the vanes compressor has an internal compression. First of all, it must be noted that many compressors start unloaded so that the approach torque is not too high. But also, when stopping, an unloaded compressor is wanted. For refrigerant compressors there is a need for regulation of flow and pressure in the function of the cooling load.