High power single frequency master oscillator fiber power amplifier is required for many applications such as coherent beam combination,gravitational wave sensors,free space optical communications,range finding,lidar and nonlinear frequency conversion. The progress of high power single frequency master oscillator fiber power amplifier is reviewed. The key techniques including seed source,stimulated Brillouin scattering suppression and amplified spontaneous emission suppression are analyzed in detail. The research trends of kilowatt levels single frequency master oscillator fiber power amplifier are pointed out.