Atmospheric escape is an essential process that affects the evolution of the proto-atmosphere. The atmospheric escape of early terrestrial planets was extremely rapid compared with the current scenarios, and the main atmospheric escape modes were also quite different. During the dissipation of the nebula disk, the primordial atmosphere experienced a brief but violent "boiling" escape, in which most of the primordial atmosphere was lost. After the nebula disk dissipates, hydrodynamic escape and impact erosion are the two most important mass-loss mechanisms for the proto-atmosphere. Hydrodynamic escape is a rapid atmospheric escape process caused by strong solar radiation, while impact erosion refers to the process in which small-large or giant impacts erode the proto-atmosphere. In the early solar system, there were other escape mechanisms, such as non-thermodynamic escape and Jeans escape, but it is generally believed that these mechanisms have relatively little impact. Here we systematically introduce the above-mentioned atmospheric escape mechanisms and then make some suggestions for the existing problems and future research for atmospheric escape models.