The discovery that supported gold nanoparticles are exceptionally effective catalysts for redox reactions has led to an explosion of interest in gold nanoparticles. In addition, incorporating a second metal as an alloy with gold can enhance the catalyst performance even more. The addition of small amounts of gold to palladium, in particular, and vice versa significantly enhances the activity of supported gold-palladium nanoparticles as redox catalysts through what researchers believe is an electronic effect. In this Account, we describe and discuss methodologies for the synthesis of supported gold-palladium nanoparticles and their use as heterogeneous catalysts. In general, three key challenges need to be addressed in the synthesis of bimetallic nanoparticles: (i) control of the particle morphology, (ii) control of the particle size distribution, and (iii) control of the nanoparticle composition. We describe three methodologies to address these challenges. First, we discuss the relatively simple method of coimpregnation. Impregnation allows control of particle morphology during alloy formation but does not control the particle compositions or the particle size distribution. Even so, we contend that this method is the best preparation method in the catalyst discovery phase of any project, since it permits the investigation of many different catalyst structures in one experiment, which may aid the identification of new catalysts. A second approach, sol-immobilization, allows enhanced control of the particle size distribution and the particle morphology, but control of the composition of individual nanoparticles is not possible. Finally, a modified impregnation method can allow the control of all three of these crucial parameters. We discuss the effect of the different methodologies on three redox reactions: benzyl alcohol oxidation, toluene oxidation, and the direct synthesis of hydrogen peroxide. We show that the coimpregnation method provides the best reaction selectivity for benzyl alcohol oxidation and the direct synthesis of hydrogen peroxide. However, because of the reaction mechanism, the sol-immobilzation method gives very active and selective catalysts for toluene oxidation. We discuss the possible nature of the preferred active structures of the supported nanoparticles for these reactions. This paper is based on the IACS Heinz Heinemann Award Lecture entitled "Catalysis using gold nanoparticles" which was given in Munich in July 2012.