In this review we analyze the current state of experiments and theory relating to the cathode spot of a vacuum arc. We discuss technical features of the experimental study of the near-cathode region of a vacuum arc with high time and space resolution. We discuss in detail the experimental data on such basic parameters characterizing the cathode spot as velocity, nature of motion, and lifetime of the spot, the current to the spot, current density, cathode fall, charge-transfer coefficient, vapor-jet velocity, charged-particle concentration, and electron temperature. We evaluate the reliability of the results obtained by various authors. A classification of cathode spots is proposed, and conditions for the existence of various types of spots and the behavior in the transition from one type to another are described. On the basis of the experimental data considered, we propose the explosive and diffusion models which provide qualitative and sometimes quantitative descriptions of cathode spots of various types.