Amorphous material usually exhibit a complex atomic structure including short-range order, long-range disorder and metastable state in thermodynamic, which is one of the existing states of matters. Amorphous alloy, also named metallic glass, is a new metallic material, and has a high strength, a good electromagnetic property, an excellent corrosionresistant and a high elasticity. The system of amorphous alloy can show some critical states and is a complicated system. In recent years, much atttentions have been paid to the researches of the phase transitions and critical phenomena of amorphous material. On a microscale, amorphous alloy can be regarded as a solid composed of many-particle systems. The investigation of the critical phenomena can significantly enhance the understanding of the interactions among these multi-particle systems. The structure of amorphous alloy is randomly and isotropic in macro performance, and ordered and anisotropic on a localized nanometer scale. The characteristics on different scales of amorphous alloy are not isolated. The structure of amorphous alloy determines the performance. The preparation process determines the nature of the microstructure. The microstructure is the internal cause dominating glass transition and deformation. Moreover, the effective cooling rate in preparation process of amorphous alloy affects the short-range rate of the amorphous phase. The nonperiodic short-range order plays a key role in the stability of amorphous phase. Furthermore, the glass transition and deformation of amorphous alloys are the responses to the external energy. The characteristics of the deformation process change with external condition. The external force can lead to the localized shear deformation and transformation between amorphous and liquid in the shear band. High temperature can cause a wide range of transformation from the amorphous solid to the liquid. So it is worth understanding in depth the basic principles of liquid and glass transition in order to prepare amorphous alloy in undercooled liquids. In this review article, we discuss the critical phenomena of amorphous alloys, which include the preparation process, the microstructure, the mechanical property and the electromagnetism. The correlation and the influence of microstructure on the macroscopic properties are analyzed. It will be helpful for understanding the nature of amorphous alloy, improving service reliability and exploring amorphous alloys with application values.