Variation laws of earth pressure accounting for the displacement of a retaining wall can be described by a mathematical fitting method. The mathematical fitting method 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. These six categories are: trigonometric function, exponential function, hyperbolic function, power function, sigmoid function and other ones. Characteristics and deficiencies of displacement-dependent earth pressure formulations are summarized, and future research focuses are provided. The findings of this study show that main differences of mathematical fitting functions are attributed to choosing function forms as well as different undetermined parameters and their magnitudes, which results in the diversity of mathematical fitting functions and the universality of research. A reasonable and practical mathematical fitting function of displacement-dependent earth pressure 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 researches 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 extendedly 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.