The aim of this contribution is to provide an overview on various models of viscoelastic materials. Specifically, based on the well known classical model, different generalisations are introduced. The mechanical response of a viscoelastic material depends on time not only through the present time, but also via its deformation history. Hence, a viscoelastic material is termed a material with memory. Accordingly, under the mathematical viewpoint, such a behaviour is modelled via the introduction of, in the evolution equations, an integral term. In viscoelasticity, such a term whose kernel represents the relaxation modulus is the key quantity to describe the behaviour of the material of interest. Different aspects are taken into account via suitable modifications of the kernel, such as weak regularity or unbounded kernels at the initial t=0 time and, in addition, effects of ageing i.e. effects of degradation of the material response due to age, are considered. When the actual response of the material is of interest, it seems important to take into account that the material response is not the same at any future time, but it is subject to change due to degradation effects. The study starts from viscoelastic materials, but, then, naturally estends to magneto-visceolastic ones. Indeed, e.g., the properties of the viscoelastic gel can be altered by embedding magnetically responsive micro or nanoparticles. Hence, the mechanical behaviour of such viscoelastic material can be modified tuning an external magnetic field. Also when magneto-viscoelastic material is considered, the study of the effects of ageing of the material itself in the determination of the mechanical response have important consequences.