Inferences of demographic history and natural selection are central themes in population genetics. Recent advances in ancestral recombination graph (ARG) inference offer new opportunities to address these long-standing problems. In the first part, I will introduce mrpast, a method that leverages ARGs for complex demographic inference. By modeling pairwise coalescence times within ARGs through a composite likelihood framework, mrpast enables accurate joint estimation of demographic parameters, including changes in effective population size, admixture proportions, migration rates, and epoch times. We apply mrpast to reconstruct the demographic histories of Eurasian and admixed American populations. In the second part, I will present PAC, a neutrality test that uses marginal coalescent trees within ARGs to identify genomic regions under selection. We show that PAC attains high power and sensitivity for detecting a range of selective scenarios, including hard, soft, partial, and ancient sweeps, as well as balancing selection. Moreover, PAC improves localization of causal variants. Together, these approaches demonstrate how rich information in ARGs can be used to improve demographic and selection inference in population genetics.