The study of microstructure-property relationships and processing history leading to those relationships is at the core of materials engineering. The historical evolution of the understanding of processing-microstructure-property relationships has largely relied on empirical evidence that, in turn, has helped catalyze theories iteratively linking modeling to experiments, which has then helped the maturation process of materials design. While the power of modeling methods has increased, we have, as of yet, no unified mathematical formalism to seamlessly connect materials chemistry with kinetics and micro- and mesoscale information despite decades of work. In this article, we provide an overview of how microstructural informatics permits one to capture the interaction between processing variables and their influence on microstructure-chemistry-property correlations. This includes a particular focus on the use of manifold representations and data compression methods for defining microstructure-chemistry-property relationships that can explain known materials behavior and aid in designing new processing pathways of materials with enhanced properties. The concept of identifying an irreducible representation of microstructure is introduced.