Infrared dim and small target detection systems can be installed into a wide range of platforms, and has important practical value in the fields of infrared early warning, guidance and so on. However, it is challenging to detect dim and small target in complex background due to the low signal to noise ratio and radical change of background. Consequently, dim and small target detection in complex background is hotspot and hard pot of related field. In this paper, the previous works on IR dim and small target detection were divided into single-frame based (including methods based on local information and nonlocal information) and multi-frame based (including methods based on associated checking and directed calculation), and further the principles, advantages and drawbacks of these methods were analyzed. Finally, the comments and predictions on the development of IR dim and small target detection in the future were provided. Our work is not only a tutorial for the beginner in terms of current works and development trends, but also a reference for other researchers.