The archaic ancestry present in the human genome has captured the imagination of both scientists and the wider public in recent years. This excitement is the result of new studies pushing the envelope of what we can learn from the archaic genetic information that has survived for over 50,000 years in the human genome. Here, we review the most recent ten years of literature on the topic of archaic introgression, including the current state of knowledge on Neanderthal and Denisovan introgression, as well as introgression from other as-yet unidentified archaic populations. We focus this review on four topics: i) a reimagining of human demographic history, including evidence for multiple admixture events between modern humans, Neanderthals, Denisovans, and other archaic populations; ii) state-of-the-art methods for detecting archaic ancestry in population-level genomic data; iii) how these novel methods can detect archaic introgression in modern African populations; and iv) the functional consequences of archaic gene variants, including how those variants were co-opted into novel function in modern human populations. The goal of this review is to provide a simple-to-access reference for the relevant methods and novel data, which has changed our understanding of the relationship between our species and its siblings. This body of literature reveals the large degree to which the genetic legacy of these extinct hominins has been integrated into the human populations of today.