The identification of active phases/centers and reaction mechanisms, structure-reactivity relationship and their dependence on reaction temperatures and pressures, are the crucial to rationale the design of the heterogeneous catalysis. However, significant challenges remain to close “the catalytic cycle”, and typically the integration of in-situ catalytic reactions of supported nano-catalysts, surface sciences and novel first principle density functional theory calculations including T/P are required. To illustrate the challenges and possible solutions based on the synergetic cooperation between bottom-up experiment and theory, CO oxidation on Pt, and preferential CO oxidation in excess of hydrogen on PtFe alloy, industrial important catalytic reactions, will be discussed. Complexity of the catalytic reactions under realistic conditions as well as “materials gap” and “pressures gap” will be illustrated. Various structural models (bimetallic alloys, core-shell, metal/metal oxide etc) under reaction conditions and their effects on the reaction mechanisms (active phases/centers, reaction path) will be explored.