Mounting evidence suggests that patterns of local relatedness can change over time in predictable ways, a process termed kinship dynamics. Kinship dynamics may occur at the level of the population or social group, where the mean relatedness across all members of the population or group changes over time, or at the level of the individual, where an individual’s relatedness to its local group changes with age. Kinship dynamics are likely to have fundamental consequences for the evolution of social behaviour and life history because they alter the inclusive fitness payoffs to actions taken at different points in time. For instance, growing evidence suggests that individual kinship dynamics have shaped the evolution of menopause and age-specific patterns of helping and harming. To date, however, the consequences of kinship dynamics for social evolution have not been widely explored. Here we review the patterns of kinship dynamics that can occur in natural populations and highlight how taking a kinship dynamics approach has yielded new insights into behaviour and life-history evolution. We discuss areas where analysing kinship dynamics could provide new insight into social evolution, and we outline some of the challenges in predicting and quantifying kinship dynamics in natural populations.