The study of the de Rham-Witt complex was initiated by Bloch, Deligne and Illusie in the 1970s in the study of the crystalline cohomology of a smooth variety over a perfect field of positive characteristic p. After that, various further developments were achieved by e.g. Langer, Zink, Hesselholt, Madsen, etc.. Recently, Bhatt, Lurie and Mathew gave a new construction of the de Rham-Witt complex of a \F_p-scheme, which is called the saturated de Rham–Witt complex. In this talk, I will introduce the concepts of a Dieudonné complex and a Dieudonné algebra, give the construction of a saturated de Rham–Witt complex for a \F_p-algebra, and discuss the comparison theorem of the saturated de Rham–Witt complex with the classical construction of Bloch-Deligne-Illusie on a smooth variety over a perfect field of characteristic p>0.