We are presenting an overview of a framework for treating material behavior and material properties as design models and variables respectively, in the context of designing materials that need to perform such as they satisfy specific data- and specification-driven performance requirements. After an overview of the general principles and strategies two examples will be presented at the opposite ends of the length scale spectrum. In the atomistic scale level we demonstrate the determination of the Lenard-Jones (L-J) potential parameters that govern the dynamics of a problem of fracture such that a specific load history of the associated medium is realized. The approach followed is that of an inverse problem. A global Monte Carlo optimizer along with a legacy molecular dynamics code are implemented on Graphical Process Unit computational infrastructure, to compute the design variables of the problem that in this case are the L-J constants. In the macro scale we demonstrate the determination of a general set of material parameters that define the elastic and inelastic (with damage) constitutive response of the general anisotropic medium applicable for fiber-epoxy composite material laminates. The specification requirements to be satisfied are those of a set of data representing load-displacement histories in the full 6-dimensional kinematic space collected via a custom-made multiaxial robotic testing machine.. The problem is also approached from an inverse problem perspective. The determination of the best suitable constitutive theory and the design (material) constants is achieved by minimizing objective functions such as the difference between experimentally measured and analytically computed system responses as described by strain fields and surface strain energy densities. Finally, examples based actual data demonstrate the successful application of design optimization for constitutive characterization.