Chemistry of a catalyst surface during catalysis is crucial for a fundamental understanding of mechanism of a catalytic reaction performed on the catalyst in the gas or liquid phase. Due to the pressure- or molecular density-dependent entropy contribution of gas or liquid phase of the reactants and the potential formation of a catalyst surface during catalysis different from that observed in an ex situ condition, the characterization of the surface of a catalyst under reaction conditions and during catalysis can be significant and even necessary for understanding the catalytic mechanism at a molecular level. Electron-based analytical techniques are challenging for studying catalyst nanoparticles in the gas or liquid phase although they are necessary techniques to employ. Instrumentation and further development of these electron-based techniques have now made in situ/operando studies of catalysts possible. New insights into the chemistry and structure of catalyst nanoparticles have been uncovered over the last decades. Herein, the origin of the differences between ex situ and in situ/operando studies of catalysts, and the technical challenges faced as well as the corresponding instrumentation and innovations utilized for characterizing catalysts under reaction conditions and during catalysis, are discussed. The restructuring of catalyst surfaces driven by the pressure of reactant(s) around a catalyst, restructuring in reactant(s) driven by reaction temperature and restructuring during catalysis are also reviewed herein. The remaining challenges and possible solutions are briefly discussed.