Heterogeneous catalysis is one of the most important chemical processes of various industries performed on catalyst nanoparticles with different sizes or/and shapes. In the past two decades, the catalytic performances of different catalytic reactions on nanoparticles of metals and oxides with well controlled sizes or shapes have been extensively studied thanks to the spectacular advances in syntheses of nanomaterials of metals and oxides. This review discussed the size and shape effects of catalyst particles on catalytic activity and selectivity of reactions performed at solid-gas or solid-liquid interfaces with a purpose of establishing correlations of size- and shape-dependent chemical and structural factors of surface of a catalyst with the corresponding catalytic performances toward understanding of catalysis at a molecular level.