The electronic and geometric structures of surfaces are closely related to each other. Conventional surface science techniques can study one or the other, but not both at the same time. Recent developments in scanning tunneling microscopy have made it possible to study simultaneously the electronic and geometric structure of Si(111) and Si(001) surfaces. Surface states can be atomically resolved in space and energy; thus the electronic structure of single atoms on surfaces can be studied in detail. The various surface states observed on silicon surfaces are found to derive from different atomic-scale features in the surface geometric structure. Scanning tunneling microscopy has now bridged the gap between electronic and geometric structure, providing a unique opportunity to obtain a better understanding of many surface processes at the atomic level.