Assessing farm animal welfare requires a good understanding of the animals' affective experiences, including their emotions. However emotions in animals can only be inferred from their behaviour because of the absence of verbal language. In addition emotions are transient reactions whereas welfare is a longer-lasting affective state. Our objective here is to highlight the two-way relationships between emotions and cognition that were originally identified in human psychology, and to describe in what ways these can be used to better access affective experiences in farm animals. A first part describes an experimental approach conducted in lambs and based on the cognitive processes that the animal can use to evaluate its environment. This approach offers an integrative and functional framework to assess the animal's emotions more effectively. A second part focuses on the influence of emotions on cognitive processes and describes recently developed methodologies based on that relationship, which may enable an assessment of long-term affective states in animals. Finally a third part discusses the relevance of behavioural strategies to improve welfare in animals by taking their cognitive skills into account. Specific cognitive processes eliciting positive emotions are emphasised. Research into animal feelings is progressing rapidly and should contribute to the development of innovative farming practices based on the animals' sentience and on their cognitive skills in order to improve their welfare.