The manuscript at hand is devoted to present constitutive formulations and finite element frameworks, which can be employed to analyze the multi-field coupled behavior of electro-active polymers and magneto-sensitive elastomers. In this contribution, electro-mechanical material coupling of anisotropic materials, thermo-electro-mechanical and thermo-magneto-mechanical material interactions are constitutively expressed, where associated material formulations are suggested. The proposed material models are implemented in finite element frameworks, which are capable of evaluating the coupled response of nearly incompressible active materials. For anisotropic electro-active materials, a transversely isotropic electro-viscoelastic material model is suggested, where the anisotropy of the mechanical, electrical and coupled electro-mechanical responses are mathematically described. The occurrence of instability in materials undergoing thermo-electro-mechanical coupling is evaluated using a computational framework, which is mainly based on the finite element method and associated eigenvalue analyses. For magneto-active polymers, a coupled thermo-magneto-viscoelastic material model is proposed and treated within a finite element framework. Several numerical simulations are performed to demonstrate the capability of the suggested constitutive formulations and computational frameworks, where in some numerical examples it is referred to coupled experiments of active materials, to identify some material model parameters. The constitutive and computational modeling approaches presented in this manuscript constitute a reference, which can be used to construct finite element-based tools for predicting the behavior of similar polymer-based active materials, where multi-field material coupling is taken into account in a relatively consistent manner.