Vacuum arc cathode spot theories are reviewed, beginning from the primary studies in second half of 19th century and in the beginning of 20th century up to the present. The evolution of the main ideas is presented, starting from those which developed for separate phenomena, up to systematic inclusive models. Different approaches were considered for generating a plasma comprised of cathode material, based on cathode vaporization and local explosions. Models with closed systems of equations were developed. A kinetic model advantageously allows calculating the cathode potential drop. These closed models explain various phenomena and spot types, based on two principals: (1) impeded plasma flow enables cathode spot operation, and (2) the heat loss in the cathode must be smaller than the energy input to the cathode spot.