Hybridization of individuals from genetically differentiated populations causes their genomes to become a mosaic of population ancestries. Widespread availability of genetic markers during the late twentieth century stimulated the development of statistical methods for inferring both recent hybrids and population admixture proportions in individuals. Newer methods focus on population ancestries of chromosomal segments in individuals (local ancestry inference or chromosome painting). We first review established statistical methods for inferring recent hybrids (specifically F 1 , F 2 , and first-generation backcrosses), individual population admixture proportions, and population ancestry of chromosome segments in individuals, focusing on the biological assumptions underlying different methods. We then discuss a canonical population genetic model, the multispecies coalescent with introgression and recombination, that connects the inference of admixture proportions with population ancestries of chromosomes. Finally, we discuss new approaches with prospects for increasing the biological realism of admixture models and improving population ancestry inference on chromosomes using techniques such as deep learning.