A better understanding of animal emotion is an important goal in disciplines ranging from neuroscience to animal welfare science. The conscious experience of emotion cannot be assessed directly, but neural, behavioural and physiological indicators of emotion can be measured. Researchers have used these measures to characterize how animals respond to situations assumed to induce discrete emotional states (e.g. fear). While advancing our understanding of specific emotions, this discrete emotion approach lacks an overarching framework that can incorporate and integrate the wide range of possible emotional states. Dimensional approaches that conceptualize emotions in terms of universal core affective characteristics (e.g. valence (positivity versus negativity) and arousal) can provide such a framework. Here, we bring together discrete and dimensional approaches to: (i) offer a structure for integrating different discrete emotions that provides a functional perspective on the adaptive value of emotional states, (ii) suggest how long-term mood states arise from short-term discrete emotions, how they also influence these discrete emotions through a bi-directional relationship and how they may function to guide decision-making, and (iii) generate novel hypothesis-driven measures of animal emotion and mood.