We show that minimization of the number of broken bonds present at the surface and a π-like bonding between the broken bonds are apparently the two keys to understanding several long-standing puzzles concerning Si surfaces. To fully exploit the above mechanisms, for both the π-bonding and elimination of broken bonds, the surface atoms must rearrange themselves rather thoroughly - namely, the surface topology and the ring structure must be altered. Based only on topological considerations and simple counting of broken bonds, the minimization of the number of broken bonds shows: why the 7×7 surface is terraced, i.e. consists of intersecting steps; why these steps (as well as steps on the cleaved surface) form only in certain crystallographic directions; why the terraces are triangular and not hexagonal; why the surface structure is symmetric 7×7 (as opposed to, e.g., 5×9); and what is the origin of the spatial scale of the 7×7 reconstruction. Of the reconstruction models proposed for the cleaved 2×1 surface, the π-bonding model leads to the largest total-energy benefit, and only the π-bonding model provides a natural interpretation of the various spectroscopic data on this surface. We show that one of the most widely used ideas in the context of semiconductor reconstruction, that of buckling, is inappropriate for homopolar semiconductors. Buckling, however, provides a valid reconstruction mechanism for heteropolar surfaces such as the GaAs(110). These conclusions are based on total-energy and surface-band calculations using the self-consistent pseudopotential method. © 1983.