Abstract: The properties and advantages of microwave imaging problem, especially the technology and algorithms of imaging in electromagnetic field were introduced in this work, and a summarized overview for the existing inverse algorithms was given. Several representative microwave imaging reconstruction algorithms were presented, including ω-k algorithm, local shape function method, Born iterative method, contrast source inversion method, particle swarm optimization and the inexact Newton method. Different algorithm were compared, in order to give their principle, characteristics and range of use. The development trend of microwave imaging algorithm was presented.