Metal-semiconductor (M-S) contacts are among the most important structural elements of modern electronic and optoelectronic systems. Their electrical properties determine the operation of diodes, transistors, sensors, microwave devices, and power electronic structures. Depending on the metal work function, semiconductor doping level, and interface quality, the contact may behave either as a rectifying Schottky barrier or as a low-resistance ohmic interface. Although classical Schottky-Mott theory successfully describes ideal contacts, practical devices often exhibit significant deviations caused by interface states, interfacial oxides, defect-assisted transport, and structural inhomogeneity of deposited metal films. The present paper provides a comprehensive theoretical analysis of the electrophysical properties of ohmic and Schottky contacts with emphasis on barrier inhomogeneity associated with metal microstructure. Classical and modern theories of barrier formation are reviewed together with current transport models based on thermionic emission, thermionic-field emission, and tunnelling. Special attention is devoted to anomalous reverse current{voltage characteristics containing multiple slopes and pronounced "kinks." A icrostructure-based interpretation is proposed in which local variations of metal work function produce spatially nonuniform barrier heights and local conductive channels. Practical recommendations for the fabrication of reliable ohmic and Schottky contacts are also discussed.