Sheet metal forming (SMF) simulations are traditionally carried out with rigid active forming surfaces. This means that the elasticity and dynamics of presses and die structures are ignored. The only geometries of the tools included in the simulations are the active forming surfaces. One reason for this simplification is the large amount of computational power that is required to solve finite element (FE) models that incorporates elastic stamping dies. Another reason is the lack of die CAD models before the later stages of stamping projects. Research during the last couple of decades indicated potential large benefits when including elastic dies in SMF simulations. For example, for simulating die try-out or for Digital Twins of presses and dies. Even though the need and potential benefits of elastic dies in simulations are well known it is not yet implemented on a wide scale. The main obstacles have been lacking data on presses and dies, long simulation times, and no standardized implementation in SMF software. This paper presents an overview of existing methods for SMF simulations with elastic dies and discuss their respective benefits and drawbacks. The survey of methods shows that simulation models with elastic tools will be needed for detailed analyses of forming operations and also for purposes like digital twins. On the other hand, simplified and robust models can be developed for non-FEA users to carry out simple one-step compensation of tool surfaces for virtual spotting purposes. The most promising and versatile method from the literature is selected, modified, and demonstrated for industrial sized dies.