A cyber-power system, a type of cyber-physical system, contains two interconnected infrastructures: a power network and a cyber network. The cyber network monitors, protects and controls the power network. Without the cyber network, the power network cannot operate efficiently or reliably. This paper studies the cyber-power interdependencies in smart grids and categorizes four types of interdependencies between cyber and power networks. The proposed classification permits the assessment of adverse effects of cyber network failures on the power network's operation. Two applications of cyber-power systems, automated substations and micro grids, are discussed in this paper, and certain cyber-power interdependencies are listed as examples.