Abstract Two individuals’ DNA is said to be identical by descent when the individuals inherited it from a shared ancestor such as a great-grandparent. Identity by descent (IBD) occurs in relatively long segments of several million base pairs when the shared ancestor lived within approximately the past 50 generations. Since ancestors from 50 generations ago can have many descendants, it is possible to find segments of IBD between many pairs of individuals without known relationships. The goal of this proposal is to develop three new applications of IBD segments. The first application is estimating recombination rates. Recombination rates vary across the genome, and the rates must be estimated in order to perform many other genetic analyses. We will develop methods that use IBD segments to estimate recombination rates from population sample data. We will also develop methods to rigorously compare IBD-based recombination maps across populations. We will estimate recombination rates in different human populations, and we will investigate regions of the genome where there are differences between populations. The second application is estimating sex-specific demographic history. Males and females can have different effective population sizes due to differing variability in reproductive success, and males and females often have different rates of migration. We will develop method to estimate sex-specific effective population sizes and mutation rates by comparing rates of IBD segments on the X chromosome (which is weighted towards female history) and the autosomes (which are equally weighted between male and female histories). This work will improve our understanding of the historical dynamics that have shaped populations. The third application is analyzing recent positive selection. Selected regions can be found by looking for elevated levels of IBD. We will develop statistical methodology to estimate the strength of selection, the mode of selection, and the frequency of the selected variants. We know that selection differs across geographic regions due to different pathogens and other environmental exposures, and we will analyze diverse populations to catalog selected regions and how they differ between populations.