The electronic properties of metal-semiconductor or Schottky contacts are characterized by their barrier heights. At ideal contacts, they are determined by the continuum of metal-induced gap states. Extrinsic interface defects and dipoles as well as interlayers may be present in real contacts and will modify the barrier heights. The zero-charge-transfer barrier height and a slope parameter describe the chemical trends of the barrier heights of Schottky contacts on a specific semiconductor. The zero-charge-transfer barrier heights may be calculated by using the empirical tight-binding method with universal parameters and the width of the dielectric band gaps and the slope parameters are given by the optical dielectric constants of the semiconductors. This is verified by comparison with numerical data from well-established theoretical approaches. Hydrogen doping of metal-diamond and metal-silicon interfaces changes their barrier heights with opposite sign. This is explained by a different orientation of H-C and H-Si interface dipoles. Ag and Pb/Si(111) contacts may be prepared with a "7x7" and a 1x1 interface structure. The difference of their barrier heights is explained by the electric dipole correlated with the stacking fault which is a characteristic of 7x7 reconstructions. Interlayers will also alter the barrier heights of Schottky contacts. Typical examples are SiO2 and Si3N4, i.e., MOS and MNS structures. Previous investigations found their barrier heights to vary as a function of the metals used. The chemical trends of these two data sets are described by the slope parameters predicted from the optical dielectric constants of SiO2 and Si3N4.