As modern and ancient DNA sequence data from diverse human populations accumulate, evidence is increasing in support of the existence of beneficial variants acquired from archaic humans that may have accelerated adaptation and improved survival in new environments - a process known as adaptive introgression. Within the past few years, a series of studies have identified genomic regions that show strong evidence for archaic adaptive introgression. Here, we provide an overview of the statistical methods developed to identify archaic introgressed fragments in the genome sequences of modern humans and to determine whether positive selection has acted on these fragments. We review recently reported examples of adaptive introgression, grouped by selection pressure, and consider the level of supporting evidence for each. Finally, we discuss challenges and recommendations for inferring selection on introgressed regions.