The electrochemical science that makes many energy conversion and storage technologies work rests on our knowledge and understanding of heterogeneous materials and material systems. The function and functionality of those systems share many common features across a wide range of technologies including fuel cells; batteries, capacitors, and membranes. The science that controls that functionality for these complex material systems is typically summoned in fragments to design a specific device. The present paper discusses an attempt to create a codified multiphysics approach to that general subject, across multiple scales in space and time, for heterogeneous functional materials, or "HeteroFoaM" as we call it. The scope of the paper will be necessarily limited to a general definition of the problem focused on a few specific examples of the progress made for directions that support technologies such as conversion of chemical energy to electricity, membranes for selective transport, and charge storage devices. The principal motivation for this approach is to establish the science that controls emergent properties in heterogeneous functional materials as a foundation for design of functional material systems with performance not bounded by constituent properties. (C) 2013 The Electrochemical Society. [DOI: 10.1149/2.012306jes] All rights reserved.