Cold and heat waves represent a significant problem for the electricity generation sector. The disruptions cold and heat waves can cause in power production are beyond their consumption impacts through, for instance, higher peak demand. Unexpected stops at thermal or nuclear power plants by excessively high-temperature water constitute clear examples of this. In this invited paper, we use past case studies to analyze the impact of these kinds of events on power production. Subsequently we discuss how events of this nature may evolve over the future in view of their association to climate change. Although the review is not exhaustive, we do expose some ideas that may be relevant for decision making in this area.