In most applications in industry involving catalysis, heterogeneous catalysts are preferred over their homogeneous counterparts when available. However, the former cannot be easily made as selective for complex chemical conversions as the latter. Selectivity requires control of the structural and electronic properties of the catalytic sites at a molecular level, and that is in general quite difficult to accomplish in solids. Nevertheless, a number of novel approaches have been advanced in recent years toward that goal. In this brief Perspective we provide a personal view of some of the avenues available to make highly selective heterogeneous catalysts. First, we discuss the possibility of tethering or otherwise immobilizing homogeneous catalysts on solid surfaces. Alternatively, molecular complexity can be added to solid surfaces via the adsorption of discrete modifiers. Isolated catalytic sites with unique molecular characteristics can also be created during or after the synthesis of heterogeneous catalysts. The structure of the exposed facets of solids can themselves be exploited to control catalytic performance. Finally, complex nanostructures such as Janus and core-shell nanoparticles can be synthesized and employed as scaffolds for multiple catalytic functionalities. A few examples of all of these methodologies, mainly from our own laboratory, are provided, and a discussion of the pros and cons of each approach is provided.