Transport of heat and diffusion of chemical species manifest themselves at various time and length scales, from femtoseconds to seconds or days and from angstroms to meters. A variety of “at-scale” experimental, theoretical, and computational tools are available to study these phenomena within narrow length and time intervals imposed by the limitations of individual techniques. However, to capture the dynamic, time-dependent characteristics of heat and chemical transport, the investigation must span multiple length and time-scales. In the experimental domain, these needs are fulfilled by optical and electronic microscopes. In the theoretical and computational domain, multi-scale computer simulations can serve as a basis for “computational microscopy”. This presentation uses at-scale and multi-scale simulations of heat transport and chemical diffusion in materials to illustrate the challenges and opportunities of multi-scale computational microscopy.