High temperature electrolysis of water and steam may provide an efficient, cost effective and environmentally friendly production of H₂ using electricity produced from sustainable, non-fossil energy sources. To achieve cost competitive electrolysis cells that are both high performing i.e. minimum internal resistance of the cell, and long-term stable, it is critical to develop electrode materials that are optimal for steam electrolysis. In this article electrolysis cells for electrolysis of water or steam at temperatures above 200 °C for production of H₂ are reviewed. High temperature electrolysis is favourable from a thermodynamic point of view, because a part of the required energy can be supplied as thermal heat, and the activation barrier is lowered increasing the H₂ production rate. Only two types of cells operating at high temperature (above 200 °C) have been described in the literature, namely alkaline electrolysis cells (AEC) and solid oxide electrolysis cells (SOEC). In the present review emphasis is on state-of-the art electrode materials and development of new materials for SOECs. Based on the state-of-the-art performance for SOECs H₂ production by high temperature steam electrolysis using SOECs is competitive to H₂ production from fossil fuels at electricity prices below 0.02–0.03 € per kWh. Though promising SOEC results on H₂ production have been reported a substantial R&D is still required to obtain inexpensive, high performing and long-term stable electrolysis cells.