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The Patch-NAH method possesses advantage in solving engineering problems, and it is especially suitable for reconstructing local sound field to obtain the acoustic parameters. After introducing the origin and basic algorithms of Patch-NAH, Patch-NAH methods are classified into four different types according to innovation extent and applicability of the methods themselves, and then, the principles, developments and current research status of the methods are introduced. The methods include the Fast Fourier Transform-based Patch-NAH, the equivalent source method-based Patch-NAH, the statistically optimized-based Patch-NAH, and the boundary element method-based Patch-NAH. Finally, the developing trend around Patch-NAH techniques is indicated.