This paper briefly discusses the writing of art criticism, art history, the relationship between art criticism and art history, and the qualities that critics should have. Art criticism is the evaluation and value judgment of art works or art phenomena based on certain standards. The emergence of art criticism is to better appreciate and understand art, and its emergence is mainly in the transition period between classical art and modern art. In the section of "Art Criticism Writing", it focuses on "What is Criticism" and several links of art criticism writing; In the section of "writing of art history", the author focuses on the logical relationship between Greenberg's thought of "dialectical transformation" and art history.