Recent years have seen the development of new ways of handling genetic data and making inferences on specific types of demographic events such as population expansions, bottlenecks, or admixture events. Indeed, simulations have shown that ancient demographic events can leave specific signatures in genetic data extracted from present‐day populations. How specific these signatures are is the focus of ongoing research. In this article, we present some of the principles underlying demographic inference based on genetic data. We discuss some results from the coalescent theory, which has been the backbone of population genetic modeling for the last 15–20 years. We also describe some of the recent methodological developments including the introduction of Bayesian and the so‐called approximate Bayesian computational methods. Genetic data provide unique and very powerful means of inferring or understanding the patterns of sometimes very ancient demographic events. However, we also emphasize the huge uncertainty in our ability to reconstruct past events from genetic data in general, and from mtDNA or Y chromosome haplotypes in particular. We conclude by discussing a number of problems associated with the use of network‐based methods, and briefly highlight some promising avenues of research for the future.