Power-to-Methane is a technically feasible process that can store large amounts of electrical energy for a long time period. The produced gas of the process can be fed into the natural gas grid or used as fuel. An essential part of the process chain is the catalytic methanation of carbon dioxide. In the methanation process, carbon dioxide and hydrogen are converted into methane and water vapor. Carbon dioxide can be won from industrial processes, ambient air or biogas plants. In this paper, fundamentals and process developments of methanation of carbon dioxide are described.