Concern for animal welfare stems from the recognition that animals are sentient beings capable of experiencing negative emotions, such as fear, pain and frustration. Fear is a major emotion in determining how animals perceive and respond to their social and physical environment. We tackle three main areas. Our first section on the assessment of fear embraces the diversity of frightening events and fear responses, various ways of assessing the fear state, the concept of fearfulness as related to temperament, and the need for stringent validation of tests and measures. Emotions are generally viewed as the result of how an individual evaluates a triggering situation according to its relevance, the likely consequences and the potential for control. Secondly, we review reported interactions between cognition and emotion and explore a possible role for cognitive ability in the assessment of emotional states: we ask whether fear-induced cognitive bias can be used to probe long-lasting affective states, and we examine the role of specific aspects, such as predictability and controllability. Thirdly, we revisit the damaging effects of fear and other negative emotions. Harmful consequences of intense and/or prolonged fear include health and welfare problems (withdrawal, injury, reduced immunocompetence, pathological anxiety), management problems (e.g. difficulty in handling and moving animals), as well as damaging effects on production, product quality and profitability. Finally, before concluding, we briefly mention the main ways of alleviating fear and the need for such strategies to be practical.