It has been believed that catalytic activity increases in direct proportion to the surface area. Recently, however, departures from this proportionality have been reported both in terms of the size and shape of catalyst particles. The size and shape effects are predominant when the particle diameter approaches the nanometer scale. Many heterogeneous catalysts consist of nanometer scale transition metal particles dispersed on a high surface area metal oxide support (e.g. Al2O3) and density functional methods are used to calculate the electronic properties of metal oxide surfaces to understand how metal nanoparticles interact with such surfaces. Further reaction rates are measured (laser desorption mass spectrometry) to develop a fundamental and quantitative understanding of how the size and shape of a metal nanoparticle impacts its catalytic activity.