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Different paradigms of multi-scale analysis and modeling in modern chemical engineering are described. First, the "sequential" (hierarchical) multi-scale mathematical modeling, which is based on the hidden assumption that the model on one level is independent of the model on the previous level; second, the multi-scale approach to a multiobjective task, in which experimental data on the different levels is obtained simultaneously, and the mathematical models are built up simultaneously as well. A new approach, the 'multi-scale characterization approach' is then proposed; it is a modification of the 'interrogative kinetics' approach recently developed on the basis of the TAP (Temporal Analysis of Products)-experiment technique. The essential features of this approach are the use of well-defined diffusion as a "measuring stick", the provision of non-steady state kinetic information, "state-defining" and "state-altering" experiments, minimal gradients of concentration for non-steady-state active materials, a special procedure to distinguish the non-steady-state activity characteristic from the transport characteristic (Y-procedure), the "Rate-Reactivity Model" as a standard form of the representation of the chemical activity of solid material. The corresponding models are mostly partial differential equations to the analysis of which computer algebra methods have been applied. This approach is related to heterogenous reactions, especially selective oxidation catalytic reactions.