Ancestral recombination graphs (ARGs) summarize the complex genealogical relationships between individuals represented in a sample of DNA sequences. Their use is currently revolutionizing the field of population genetics and is leading to the development of powerful new methods to elucidate individual and population genetic processes, including population size history, migration, admixture, recombination, mutation and selection. In this Review, we introduce the readers to the structure of ARGs and discuss how they relate to processes such as recombination and genetic drift. We explore differences and similarities between methods of estimating ARGs and provide concrete illustrative examples of how ARGs can be used to elucidate population-level processes.