Liquid hydrogen is the main fuel of large-scale low-temperature heavy-duty rockets, and has become the key direction of energy development in China in recent years. As an important application carrier in the large-scale storage and transportation of liquid hydrogen, liquid hydrogen cryogenic storage and transportation containers are the key equipment related to the national defense security of China’s aerospace and energy fields. Due to the low temperature of liquid hydrogen (20 K), special requirements have been put forward for the selection of materials for storage and transportation containers including the adaptability of materials in a liquid hydrogen environment, hydrogen embrittlement characteristics, mechanical properties, and thermophysical properties of liquid hydrogen temperature, which can all affect the safe and reliable design of storage and transportation containers. Therefore, it is of great practical significance to systematically master the types and properties of cryogenic materials for the development of liquid hydrogen storage and transportation containers. With the wide application of liquid hydrogen in different occasions, the requirements for storage and transportation container materials are not the same. In this paper, the types and applications of cryogenic materials commonly used in liquid hydrogen storage and transportation containers are reviewed. The effects of low-temperature on the mechanical properties of different materials are introduced. The research progress of cryogenic materials and low-temperature performance data of materials is introduced. The shortcomings in the research and application of cryogenic materials for liquid hydrogen storage and transportation containers are summarized to provide guidance for the future development of container materials. Among them, stainless steel is the most widely used cryogenic material for liquid hydrogen storage and transportation vessel, but different grades of stainless steel also have different applications, which usually need to be comprehensively considered in combination with its low temperature performance, corrosion resistance, welding performance, and other aspects. However, with the increasing demand for space liquid hydrogen storage and transportation, the research on high specific strength cryogenic materials such as aluminum alloy, titanium alloy, or composite materials is also developing. Aluminum alloy liquid hydrogen storage and transportation containers are widely used in the space field, while composite materials have significant advantages in being lightweight. Hydrogen permeation is the key bottleneck of composite storage and transportation containers. At present, there are still many technical problems that have not been solved.