This paper raises the issue of whether nuclear power can play a flexible role within an electricity system. It does not deal with the issue of whether nuclear power should play such a role, but it does examine why in most cases it does not. We introduce the basics of nuclear physics and reactor designs sufficient to cover the technical issues of relevance. We then identify the key technical issues that must be tackled in order to load-follow with nuclear power. We assess the flexibility and load-following ability of current and future promising reactors. We confirm that modern Generation III and III+ are technically capable of flexible operation. To explain why nuclear power is almost exclusively used as baseload generation, we look at power market economics. As a result, we conclude that despite some technical abilities, nuclear power plants are preferentially used for baseload generation for economic reasons and will continue to be used in this way for the foreseeable future.