Individual animals behave differently from one another, especially when confronting challenges such as changes in diet (e.g. weaning), environment (e.g. moving from pasture to feedlot) and social grouping (e.g. movement to lactating group after parturition). Each of these challenges involves some element of novelty, impacting the welfare and productivity of the animal. Indeed, the large individual variability in the development and expression of feeding behaviour cannot be fully explained by differences in genetics, management practices, body size or growth rate. In this review we outline evidence that individual variability in feeding behaviour is associated with the personality of the individual. We focus on three key personality traits: exploration, fear or reactivity and sociability. Individuals differ in how much they explore their feeding environment, with more exploratory individuals being less reactive to novel situations. Feeding behaviour can be impaired in individuals that are especially reactive to a change in their environment, change in diet or handling or restraint by humans. The social environment is also a major factor affecting how individuals express their behaviour. Sociability of the individual, including dominant-subordinate and affiliative relationships, affects how individuals make foraging decisions, gain access to feed and adopt particular social strategies to maintain or adjust feeding patterns when the social environment changes. Personality traits such as exploration, boldness and sociability also affect the use of social information when learning where, how or what to eat. Our review highlights the implications of feeding behaviour variability for the welfare and productivity of the individual, and how an understanding of personality can help tailor management to the needs of the individual.