The nature and neural implementation of emotions is the subject of vigorous debate. Here, we use Bayesian decision theory to address key complexities in this field and conceptualize emotions in terms of their relationship to survival-relevant behavioural choices. Decision theory indicates which behaviours are optimal in a given situation; however, the calculations required are radically intractable. We therefore conjecture that the brain uses a range of pre-programmed algorithms that provide approximate solutions. These solutions seem to produce specific behavioural manifestations of emotions and can also be associated with core affective dimensions. We identify principles according to which these algorithms are implemented in the brain and illustrate our approach by considering decision making in the face of proximal threat.