This cumulative dissertation deals in a broader sense with the question under what conditions continuum-mechanical material models have predictive power. The thesis consists of an essay and four scientific publications which examine this topic from a variety of perspectives. At its core, two overarching themes emerge: (i) the task of constraining constitutive laws so as to provide a physically reasonable material response for all admissible deformation paths, and (ii) the interplay of constitutive theory and mechanical testing as it relates to the interpretation and use of experimental measurements. Concerning the former, we discuss – among other things – constitutive inequalities for hyperelasticity and the thermodynamic consistency of a damage model for the Mullins effect. The results and ensuing discussions reveal why it is important to devise constitutive laws in the context of a general three-dimensional deformation in time and space, not just a preconceived selection of standard loading scenarios. We also find that the physical implications of common constitutive constraints are not as obvious as one might expect. In relation to the interaction of theory and experiment, we give a critique of the use of neural networks and mechanically preconditioned data for the purposes of material modeling. These topics illustrate that the acquisition and interpretation of experimental measurements are highly dependent on underlying theoretical considerations. Therewith related is the task of calibration once a functional form for a material model has been selected. In this context, we establish a Bayesian framework which demonstrates the ambiguity of selecting any particular set of parameters in light of necessarily finite experimental data. In summary, the thesis highlights conceptual and practical challenges for material modeling with consequences for the predictive power of constitutive laws in continuum mechanics.