Cover crops provide agro-ecological services like erosion control, improvement of soil quality, reduction of nitrate leaching and weed control. Before planting the subsequent cash crop, cover crops need to be terminated with herbicides, mechanically or with the help of frost (winterkill). Winterkill termination is expected to increase its relevance in the next years, especially for organic farming due to limitations in the use of herbicides and for conservation agriculture cropping systems. Termination by frost depends on complex interactions between genotype, development stage and weather conditions. To understand these interactions for management purposes, crop frost damage models, whose review is the purpose of this article, can be very useful. A literature search led to the collection of eight frost damage models, mainly dedicated to winter wheat. Three of these models are described in detail because they appear suited to adaptation to cover crops. Indeed, they explicitly simulate frost tolerance acquisition and loss as influenced by development stage using a crop frost tolerance temperature, whose rate of variation depends on the processes of hardening and dehardening. This tolerance temperature is compared daily with environmental temperature to calculate frost damage to the vegetative organs. The three models, when applied to winter wheat in Canada, Norway and France, have shown good agreement between measured and simulated crop frost tolerance temperature (when declared, the root mean squared error was 2.4°C). To compare the behaviour of these models, we applied them in two locations with different climatic conditions (temperate climate: Sant’Angelo Lodigiano, Italy, and continental climate: Saskaatoon, Canada) with respect to frost tolerance acquisition. This comparison revealed that the three models provide different simulated dates for the frost damage event in the continental site, while they are more similar in the temperate site. In conclusion, we have shown that the reviewed models are potentially suitable for simulating cover crop frost damage. Highlights - Frost termination is very important for cover crops and needs to be simulated with crop models. - Lacking a cover crop frost damage model, we review eight models simulating damage of cash crops, namely cereals. - Three of these models are also applicable to cover crops and are described in more detail. - The simulated crop frost tolerance temperature decreases and increases with hardening and dehardening, respectively. - This tolerance temperature is compared with environmental temperature to calculate frost damage to the crop.