Docker exec is a useful command that allows users to run commands inside running containers, which can be helpful for debugging and troubleshooting container problems or performing one-off maintenance tasks. The syntax of the docker exec command involves identifying the container by ID or name, followed by the command to invoke. Some common use cases include running maintenance commands, testing network connectivity, inspecting a container's filesystem, and debugging issues with containers. However, it is important to use docker exec judiciously as starting additional processes in a container can break containerization principles. The Docker exec command supports various options such as detaching from the container command, setting environment variables, changing the user, and altering the working directory.