Animal welfare concerns stem from recognition of the fact that animals can experience emotions such as pain or joy. Nevertheless, discussion of animal emotions is often considered anthropomorphic, and there is a clear need to use explanatory frameworks to understand animals' emotions. We borrowed appraisal theories developed in cognitive psychology to study sheep emotions. Emotions are viewed as the result of how an individual evaluates a triggering situation, following a sequence of checks, including the relevance of the situation (its suddenness, familiarity, predictability, and intrinsic pleasantness), its implications for the individual (including consistency with the individual's expectations), the potential for control, and both internal and external standards. We assumed that if the outcome of checks has an impact on the animal's emotional responses, then animals do not only show emotional responses but also feel emotions. We showed that sheep use similar checks to those used by humans to evaluate their environment, ie suddenness, familiarity, predictability, consistency with expectations, and control. Furthermore, this evaluation affects their emotional responses (behavioural responses, such as startle, ear postures, and cardiac activity). It is concluded that sheep are able to experience emotions such as fear, anger, rage, despair, boredom, disgust and happiness because they use the same checks involved in such emotions as humans. For instance, despair is triggered by situations which are evaluated as sudden, unfamiliar, unpredictable, discrepant from expectations, and uncontrollable, whereas boredom results from an overly predictable environment, and all these checks have been found to affect emotional responses in sheep. These results have implications for animal welfare: although a completely invariable and totally predictable environment should be avoided to prevent boredom, sudden events should probably be minimised, the animals should be offered the possibility to control their environment, and care should be taken to ensure a degree of predictability concerning the various events.