Dynamic range compression of infrared images is an important research direction in the field of infrared image visualization. The dynamic range compression algorithm directly determines the important visualization indexes of the original infrared image, such as detail retention and overall perception; in a sense, it is the basis and guarantee of detail enhancement. This study investigates a wide dynamic range compression algorithm and a local compression algorithm based on a global compression algorithm. Based on the two algorithms, we study and analyze the development process and the advantages and disadvantages to improve the research direction and development trend, which will provide a reference for researchers.