I will start by presenting a coercivity tool which combines micromagnetics and nonlinear stability analysis to predict hysteresis in magnetic alloys and thereby provides crucial insights into the longstanding permalloy problem in soft magnets. I will then share some work on the collective evolution of polarization patterns in ferroelectrics under varying surface energy and designed electrical conductivity conditions to achieve enhanced energy conversion. Finally, I will provide an overview of how we draw inspiration from shape memory alloys to design microstructures that mitigate degradation in intercalation materials. Throughout, I show how developing multi-physics and multi-scale mathematical methods (e.g., phase-field methods, phase-field crystal methods, and objective molecular dynamics) allows questions about how microstructure impacts material properties to be addressed.