The assessment of farm animal welfare requires a good understanding of the animals' affective experiences, including their emotions. Emotions are transient reactions to short-term triggering events and can accumulate to cause longer-lasting affective states, which represent good or bad welfare. Cognition refers to the mechanisms by which animals acquire, process, store and act on information from the environment. The objective of this paper 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. The first section describes a recent experimental approach based on the cognitive processes that the animal uses to evaluate its environment. This approach offers an integrative and functional framework to assess the animal's emotions more effectively. The second section 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. The last section discusses the relevance of behavioural strategies to improve welfare in animals by taking their cognitive skills into account. Specific cognitive processes eliciting positive emotions will be emphasised. Research into affective states of animals is progressing rapidly and the ability to scientifically access animal feelings should contribute to the development of innovative farming practices based on the animals' sentience and their cognitive skills in order to truly improve their welfare