The decarbonization of industrial process heat is one of the bigger challenges of the global energy transition. Process heating accounts for about 20% of final energy demand in Germany, and the situation is similar in other industrialized nations around the globe. Process heating is indispensable in the manufacturing processes of products and materials encountered every day, ranging from food, beverages, paper and textiles, to metals, ceramics, glass and cement. At the same time, process heating is also responsible for significant greenhouse gas emissions, as it is heavily dependent on fossil fuels such as natural gas and coal. Thus, process heating needs to be decarbonized. This review article explores the challenges of decarbonizing industrial process heat and then discusses two of the most promising options, the use of electric heating technologies and the substitution of fossil fuels with low-carbon hydrogen, in more detail. Both energy carriers have their specific benefits and drawbacks that have to be considered in the context of industrial decarbonization, but also in terms of necessary energy infrastructures. The focus is on high-temperature process heat (>400 °C) in energy-intensive basic materials industries, with examples from the metal and glass industries. Given the heterogeneity of industrial process heating, both electricity and hydrogen will likely be the most prominent energy carriers for decarbonized high-temperature process heat, each with their respective advantages and disadvantages.