The assumption that animals are conscious and capable of experiencing negative sensations and emotions is at the core of most people's concerns about animal welfare. Investigation of this central assumption should be one goal of animal welfare science. We argue that theory and techniques from cognitive science offer promising ways forward. Evidence for the existence of conscious and non-conscious cognitive processing in humans has inspired scientists to search for comparable processes in animals. In studies of metacognition and blindsight, some species show behaviour that has functional parallels with human conscious cognitive processing. Although unable to definitively answer the question of whether the animals are conscious, these studies provide fresh insights, and some could be adapted for domestic animals. They mark a departure from the search for cognitive complexity as an indicator of consciousness, which is based on questionable assumptions linking the two. Accurate assessment of animal emotion is crucial in animal welfare research, and cognitive science offers novel approaches that address some limitations of current measures. Knowledge of the relationship between cognition and emotion in humans generates a priori frameworks for interpreting traditional physiological and behavioural indicators of animal emotion, and provides new measures (eg cognitive bias) that gauge positive as well as negative emotions. Conditioning paradigms can be used to enable animals to indicate their emotional state through operant responses. Although evidence for animal consciousness and emotion will necessarily be indirect, insights from cognitive science promise further advances in our understanding of this fundamentally important area in animal welfare science.