This work addresses the large strain behaviors of thermoplastic polyurethanes (TPUs) spanning a range of fractions of hard and soft contents in both experiment and theoretical modeling. The key mechanical features involve a combination of elasticity and inelasticity, and are quantified experimentally under a broad variety of loading scenarios. A finite deformation constitutive model is then presented to capture the main features of the stress-strain data, which are strongly dependent on fractions of hard and soft contents. The stress-strain behavior of these TPUs is characterized by highly nonlinear rate-dependent hyperelastic-viscoplasticity, in which substantial energy dissipation is accompanied by shape recovery as well as softening. Agreement between the model and the experimental data for the representative TPUs provides physical insight into the underlying deformation mechanisms in this important class of soft materials that exhibit both elastomeric and plastomeric characteristics.