Every thought is associated with a unique pattern of brain activity. Thus, in principle, it should be possible to use these activity patterns as "brain fingerprints" for different thoughts and to read out what a person is thinking based on their brain activity alone. Indeed, using machine learning considerable progress has been made in such "brainreading" in recent years. It is now possible to decode which image a person is viewing, which film sequence they are watching, which emotional state they are in or which intentions they hold in mind. This talk will provide an overview of the current state of the art in brain reading. It will also highlight the main challenges and limitations of this research field. For example, mathematical models are needed to cope with the high dimensionality of potential mental states. Furthermore, the ethical concerns raised by (often premature) commercial applications of brain reading will also be discussed.