This dissertation reports four theoretical studies of electrons and phonons at nonideal semiconductor surfaces--i.e., surfaces containing defects and surfaces exhibiting geometrical reconstruction of the atoms. These studies are relevant to two of the most interesting problems in semiconductor physics: the mechanisms accounting for Schottky barriers and Ohmic contacts, and the reconstruction of polar semiconductor surfaces. (A polar surface is one consisting entirely of atoms of one species--e.g., only Ga atoms or only As atoms in the case of GaAs. The inherent instability of such a surface acts as a driving force that produces reconstruction.) The studies are the following: (1) Calculations of the deep electronic energy levels associated with dangling bonds at III-V semiconductor surfaces, using a simple model. (2) Detailed calculations of deep electronic energy levels for defect complexes at the relaxed (110) surfaces of III-V semiconductors. Defect complexes are known to occur in semiconductors, and are in fact often more important than point defects. It is therefore likely that defect complexes are in some cases responsible for Schottky barrier formation. (3) Calculations of the effects of alloy broadening on deep electronic energy levels and Schottky barrier heights for various defects at III-V semiconductor surfaces, again using a simple model. (4) Detailed calculations of surface phonons for the Tong vacancy-reconstructed model of the (111) (2 x 2) surfaces of III-V semiconductors. This is the first nontrivial reconstruction of a compound semiconductor surface to be strongly indicated by experiment. Our results show that there exist several surface phonon branches below the band of the acoustic modes and between the bands of acoustic modes and optical modes. These surface phonon modes should be observable in electron energy loss spectroscopy (EELS) measurements. They should also provide a distinctive signature of the surface geometry.