Abstract: Tubular structures such as circular tubes and square tubes under axial compression, are widely used as structural components in engineering applications. Considering the difference of tube geometries, boundary conditions and material properties, we classify the failure of tubes under axial compression into 5 different mechanisms: progressive buckling, global buckling, inversion, expansion and splitting. In this paper, the theoretical, experimental and numerical studies about the different failure modes of tubes under axial compression are reviewed, and the mechanical responses and energy absorption properties are compared and discussed.