Gene families evolve by the processes of speciation (creating orthologs), gene duplication (paralogs), and horizontal gene transfer (xenologs), in addition to sequence divergence and gene loss. Orthologs in particular play an essential role in comparative genomics and phylogenomic analyses. With the continued sequencing of organisms across the tree of life, the data are available to reconstruct the unique evolutionary histories of tens of thousands of gene families. Accurate reconstruction of these histories, however, is a challenging computational problem, and the focus of the Quest for Orthologs Consortium. We review the recent advances and outstanding challenges in this field, as revealed at a symposium and meeting held at the University of Southern California in 2017. Key advances have been made both at the level of orthology algorithm development and with respect to coordination across the community of algorithm developers and orthology end-users. Applications spanned a broad range, including gene function prediction, phylostratigraphy, genome evolution, and phylogenomics. The meetings highlighted the increasing use of meta-analyses integrating results from multiple different algorithms, and discussed ongoing challenges in orthology inference as well as the next steps toward improvement and integration of orthology resources.