Photoemission electron microscopy (PEEM) has revealed a rich variety of spatiotemporal patterns, ranging from reaction fronts and spiral waves to standing waves and chemical turbulence, during the catalytic oxidation of CO as well as the reduction of NO on various Pt single crystal surfaces. More recent experiments have focused on the spatiotemporal dynamics of these catalytic reactions on microstructured and microcomposite reacting domains, constructed using microelectronics fabrication techniques. Representative domain scales for these surfaces are in the micrometer range, comparable to the typical wavelengths of concentration patterns on the clean catalytic surface. In this work we present computational and experimental studies of the effect of microcomposite surface geometry and properties on catalytic reaction dynamics. Controlled surface heterogeneities can gradually suppress certain types of reaction patterns; they can also act as "pacemakers" for the catalytic surface. The composite surface will, under some conditions, appear as a uniform "effective medium" with behavior different than that observed on each of its individual components; this can also be accompanied by significant changes in the overall reaction rate.