Based on the research achievements of tensile creep at elevated temperature, tensile creep and compression creep at room temperature, this article reviews the behavior and mechanism of compression creep of titanium alloys. The differences between creep at room temperature and elevated temperature are also introduced. Based on the observation and analysis on microstructure after creep, the main mechanism involved in the diffusion-controlled creep process, such as dislocation movement, saturated creep and so on, are compared. It is pointed out that there is a stress threshold in the room temperature creep of titanium alloys. And the high stress induced compression creep mechanism of titanium alloys at room temperature is also analyzed. Meanwhile, the main problems and difficulties on the compression creep of deepsea equipment titanium alloys are overviewed and analyzed.