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Let A be a general expansive matrix on Rn.The aims of this article are twofold.The first one is to give a survey on the recent developments of anisotropic Hardy-type function spaces on Rn,including anisotropic Hardy-Lorentz spaces,anisotropic variable Hardy spaces and anisotropic variable Hardy-Lorentz spaces as well as anisotropic Musielak-Orlicz Hardy spaces.The second one is to correct some errors and seal some gaps existing in the known articles.Some unsolved problems are also presented.