The use of architecture built into materials has led to the development of mechanical and acoustic metamaterials, which have enabled extraordinary and unprecedented manipulation of material properties (both static and dynamic). A broad degree of tailorability has been shown in these materials, but challenges have remained, chiefly among them the application to full scale dynamics and high strain rates. Herein these challenges are grouped into three broad categories: the challenge of inverse design processes for the mesostructured, the challenge of incorporating wave effects into the inverse design, and the challenge posed by the incorporation of high strain rate effects into modeling and design. A deep dive into these challenges is undertaken, exploring each of them in more detail. Both modeling and experiments are used to make strides in addressing the challenges of inverse design and wave effects, in which an inverse design framework coupled with a reduced order discrete element model is proposed and implemented. Experimental work is then undertaken to more thoroughly explore the challenges posed by high strain rates. Through these efforts this work advances toward the goal of inversely designed high strain rate metamaterials.