Variation laws of earth pressure accounting for the displacement of a retaining wall can be well described by mathematical fitting, which is usually based on the earth pressure at rest or the active and passive earth pressures to illustrate the displacement-earth pressure of retaining walls through constructing various mathematical functions. This study subdivides displacement-dependent earth pressure formulations into six categories according to different functional forms, including trigonometric, exponential, hyperbolic, power, sigmoid and other functions. Characteristics and deficiencies of displacement-dependent earth pressure formulations are summarized, and future researches are provided. The findings of this study show that main differences of mathematical fitting are attributed to determination of function forms as well as undetermined parameters as well as their magnitudes, which results in the uncertainty of mathematical fitting and the generallity of research. A reasonable and practical mathematical fitting function has three features:boundary condition and initial value satisfied, parameters with clear meaning and representing the interaction between a retaining wall and soils. In terms of test studies, it is necessary to perform targeted research on different movement modes of a retaining wall, and model tests of earth pressure are conducted on clay, unsaturated soil, collapsible loess, expansive soil, among others. In terms of theoretical calculations, displacement-dependent earth pressure formulations using different mathematical fitting functions are compared to explore their rationality and applicability as well as to reveal intrinsic mechanisms between earth pressure of a retaining wall and its displacement. Displacement-dependent earth pressure of a retaining wall in unsaturated soil needs to be paid more attention. The choice and measurement of different parameters are improved and validated by model tests in order to accelerate the process of engineering applications for mathematical fitting functions.