Rubber-like materials exhibit pronounced viscoelasticity, history dependence and stress-softening effects such as the Mullins effect, which are difficult to capture robustly with conventional phenomenological constitutive models. Classical approaches often require extensive parameter calibration and show limited flexibility for complex loading histories. Neural-network-based constitutive models provide increased expressiveness, but must satisfy fundamental mechanical requirements to be physically admissible. This contribution investigates physics-augmented neural network formulations for viscoelastic rubber-like materials. Different modeling strategies are considered, including neural representations of the Helmholtz free energy, dissipation potentials, and evolution laws for internal variables governing time-dependent and damage-like effects. Physical constraints such as thermodynamic consistency (including non-negative dissipation), objectivity, stress-free reference configurations, correct small-strain limits, and polyconvexity are enforced either by construction or through physics-informed neural network (PINN) formulations. Recurrent neural network architectures are also employed to capture history-dependent behavior. Comparisons with classical viscoelastic and Mullins-type models under cyclic and relaxation loading illustrate the capabilities and limitations of the proposed approaches and highlight the benefits of combining neural networks with physically grounded constitutive structure.