Recent studies of animal personality have focused on its proximate causation and its ecological and evolutionary significance, but have mostly ignored questions about its development, although an understanding of the latter is highly relevant to these other questions. One possible reason for this neglect is confusion about many of the concepts and terms that are necessary to study the development of animal personality. Here, we provide a framework for studying personality development that focuses on the properties of animal personality, and considers how and why these properties may change over time. We specifically focus on three dimensions of personality: (1) contextual generality at a given age or time, (2) temporal consistency in behavioural traits and in relationships between traits, and (3) the effects of genes and experience on the development of personality at a given age or life stage. We advocate using a new approach, contextual reaction norms, to study the contextual generality of personality traits at the level of groups, individuals and genotypes, show how concepts and terms borrowed from the literature on personality development in humans can be used to study temporal changes in personality at the level of groups and individuals, and demonstrate how classical developmental reaction norms can provide insights into the ways that genes and experiential factors interact across ontogeny to affect the expression of personality traits. In addition, we discuss how correlations between the effects of genes and experience on personality development can arise as a function of individuals' control over their own environment, via niche-picking or niche-construction. Using this framework, we discuss several widely held assumptions about animal personality development that still await validation, identify neglected methodological issues, and describe a number of promising new avenues for future research.