The ancestral recombination graph (ARG) is a structure that represents the history of coalescent and recombination events connecting a set of sequences (Hudson RR. In: Futuyma D, Antonovics J, editors. Gene genealogies and the coalescent process. In: Oxford Surveys in Evolutionary Biology; 1991. p. 1 to 44.). The full ARG can be represented as a set of genealogical trees at every locus in the genome, annotated with recombination events that change the topology of the trees between adjacent loci and the mutations that occurred along the branches of those trees (Griffiths RC, Marjoram P. An ancestral recombination graph. In: Donnelly P, Tavare S, editors. Progress in population genetics and human evolution. Springer; 1997. p. 257 to 270.). Valuable insights can be gained into past evolutionary processes, such as demographic events or the influence of natural selection, by studying the ARG. It is regarded as the "holy grail" of population genetics (Hubisz M, Siepel A. Inference of ancestral recombination graphs using ARGweaver. In: Dutheil JY, editors. Statistical population genomics. New York, NY: Springer US; 2020. p. 231-266.) since it encodes the processes that generate all patterns of allelic and haplotypic variation from which all commonly used summary statistics in population genetic research (e.g. heterozygosity and linkage disequilibrium) can be derived. Many previous evolutionary inferences relied on summary statistics extracted from the genotype matrix. Evolutionary inferences using the ARG represent a significant advancement as the ARG is a representation of the evolutionary history of a sample that shows the past history of recombination, coalescence, and mutation events across a particular sequence. This representation in theory contains as much information, if not more, than the combination of all independent summary statistics that could be derived from the genotype matrix. Consistent with this idea, some of the first ARG-based analyses have proven to be more powerful than summary statistic-based analyses (Speidel L, Forest M, Shi S, Myers SR. A method for genome-wide genealogy estimation for thousands of samples. Nat Genet. 2019:51(9):1321 to 1329.; Stern AJ, Wilton PR, Nielsen R. An approximate full-likelihood method for inferring selection and allele frequency trajectories from DNA sequence data. PLoS Genet. 2019:15(9):e1008384.; Hubisz MJ, Williams AL, Siepel A. Mapping gene flow between ancient hominins through demography-aware inference of the ancestral recombination graph. PLoS Genet. 2020:16(8):e1008895.; Fan C, Mancuso N, Chiang CWK. A genealogical estimate of genetic relationships. Am J Hum Genet. 2022:109(5):812-824.; Fan C, Cahoon JL, Dinh BL, Ortega-Del Vecchyo D, Huber C, Edge MD, Mancuso N, Chiang CWK. A likelihood-based framework for demographic inference from genealogical trees. bioRxiv. 2023.10.10.561787. 2023.; Hejase HA, Mo Z, Campagna L, Siepel A. A deep-learning approach for inference of selective sweeps from the ancestral recombination graph. Mol Biol Evol. 2022:39(1):msab332.; Link V, Schraiber JG, Fan C, Dinh B, Mancuso N, Chiang CWK, Edge MD. Tree-based QTL mapping with expected local genetic relatedness matrices. bioRxiv. 2023.04.07.536093. 2023.; Zhang BC, Biddanda A, Gunnarsson ÁF, Cooper F, Palamara PF. Biobank-scale inference of ancestral recombination graphs enables genealogical analysis of complex traits. Nat Genet. 2023:55(5):768-776.). As such, there has been significant interest in the field to investigate 2 main problems related to the ARG: (i) How can we estimate the ARG based on genomic data, and (ii) how can we extract information of past evolutionary processes from the ARG? In this perspective, we highlight 3 topics that pertain to these main issues: The development of computational innovations that enable the estimation of the ARG; remaining challenges in estimating the ARG; and methodological advances for deducing evolutionary forces and mechanisms using the ARG. This perspective serves to introduce the readers to the types of questions that can be explored using the ARG and to highlight some of the most pressing issues that must be addressed in order to make ARG-based inference an indispensable tool for evolutionary research.