An overview on viscoelasticity, models is presented. Specifically, aiming to model variety of new materials, such as biological or new materials, different forms of the relaxation modules are considered. To start with, the mathematical setting behind the mechanical behaviour of viscoelastic materials is briefly recalled. Notably, the mechanical responce to an external stress depends not only on the machanical status of the material at the current time, but also on its past history. Hence, the model equation is integro-differential. A crucial role is played by the relaxation modulus whose form is chosen to better describe the material under investigation. Various different forms of the relaxation modulus are examined starting from the classical model and, then, considering different generalisations, introduced to describe non-standard behaviours. Thus, a relaxation modulus, which is unbounded, or not as smooth as classically assumed is considered [1]. Then, also the effects of aging, namely the change of the mechanical response due to changes in the materials itself are modeled. Finally, a brief mention on magneto-viscoelastic models is provided. Indeed, motivated by new and smart materials in which micro or nano particles magnetically sensible can be injected, the effect of the presence of an external magnetic field is introduced in the model which, analytically, is then, represented by the coupling of a linear integro-differential equation with a non linear differential equation [2]. The effect of aging can be also taken into account [3]. REFERENCES [1] S. Carillo, M. Chipot, G. Vergara Caffarelli, A viscoelastic integro-differential equation with a discountinuos memory kernel, in progress. [2] S. Carillo, M. Chipot, V. Valente, G. Vergara Caffarelli, A magneto-viscoelasticity problem with a singular memory kernel, Nonlinear Analysis Series B: Real World Applications, 35C, 200–210, (2017). [3] S. Carillo, C. Giorgi, A magneto-viscoelasticity problem with aging, Materials, MDPI, Basel, (2022).