Soft synthetic and natural polymeric-based materials offer particular new avenues for the design and fabrication of materials and devices. Engineering the molecular and geometrical structures of the constituent materials, together with utilizing their ability to sustain large deformations enables materials and designs with novel properties and functional behavior. We begin with the development of physically-based models of elastomeric mechanics, from the elegant simplicity of the “8-chain” network model of rubber elasticity to the more complex enhancements that capture the molecular mechanisms of nonlinear time-dependent behavior. We also address the behavior of versatile co-polymers, which can form micro-composites of “hard” and “soft” domains, providing an ability to engineer unique combinations of highly resilient elastic and dissipative systems. The structure and behavior of natural analogs such as mussel byssal threads are included and shown to yield further insights. Finally, we present the ability to tailor constituent geometrical features of soft composites using new fabrication techniques including 3D printing. Exemplars include patterned and layered structures which exhibit deformation and instability-induced pattern transformations. These structural transformations result in concomitant changes in a multitude of behaviors giving super-elastic and multi-linear elastic response, enhanced mechanisms for energy storage, switchable band gaps, soft actuators, and morphable surface topology. Looking to the future, the predictive ability of multi-scale nonlinear mechanics of soft materials, combined with the rapid developments in fabrication techniques provide profound opportunities to truly design functional materials, devices and products.