The response of soils to applied loading is affected by the current state of stress and previous loading history. To account for this when evaluating their response to cyclic or dynamic loading, it is necessary to track the state of stress at each given time. Cyclic degradation or hardening of soils results in an increase or decrease in soil stiffness and strength. This is as a result of changes in the effective confining stress due to void ratio or pore pressure changes. Therefore, all cyclic soil response models account for this effect in an implicit or an explicit manner by tracking a specified memory parameter. For most empirical models, the state parameter is usually related to the number of uniform or equivalent uniform loading cycles experienced by the soil. This paper discusses various implementations of such models in the literature from a general fatigue framework point of view. Various unique features of the models are highlighted to show their capabilities, underlying assumptions and limitations.