The structure of catalysts determines the performance of catalytic processes. Intrinsically, the electronic and geometric structures influence the interaction between active species and the surface of the catalyst, which subsequently regulates the adsorption, reaction, and desorption behaviors. In recent decades, the development of catalysts with complex structures, including bulk, interfacial, encapsulated, and atomically dispersed structures, can potentially affect the electronic and geometric structures of catalysts and lead to further control of the transport and reaction of molecules. This review describes comprehensive understandings on the influence of electronic and geometric properties and complex catalyst structures on the performance of relevant heterogeneous catalytic processes, especially for the transport and reaction over structured catalysts for the conversions of light alkanes and small molecules. The recent research progress of the electronic and geometric properties over the active sites, specifically for theoretical descriptors developed in the recent decades, is discussed at the atomic level. The designs and properties of catalysts with specific structures are summarized. The transport phenomena and reactions over structured catalysts for the conversions of light alkanes and small molecules are analyzed. At the end of this review, we present our perspectives on the challenges for the further development of structured catalysts and heterogeneous catalytic processes.