As the core nonlinear component of block ciphers, functions over finite fields rely on their low differential uniformity to resist differential cryptanalysis. Almost Perfect Nonlinear (APN) functions, renowned for their optimal differential properties, have become a research focus in this field. This paper systematically reviews the research progress of APN functions: first, it summarizes the general methods for generating APN function examples; second, it refines the construction techniques of existing infinite families of APN functions and clarifies their specific constructions; third, it introduces the equivalence classification results of APN function examples and infinite families; fourth, it combs through the research conclusions on the cryptographic properties of APN functions, such as permutation property, algebraic degree, and nonlinearity; fifth, it reviews some applications of APN functions in coding theory and combinatorial design; Finally, the research prospects of APN functions are prospected.