Comparisons of DNA from archaic and modern humans show that these groups interbred, and in some cases received an evolutionary advantage from doing so. This process - adaptive introgression - may lead to a faster rate of adaptation than is predicted from models with mutation and selection alone. Within the last couple of years, a series of studies have identified regions of the genome that are likely examples of adaptive introgression. In many cases, once a region was ascertained as being introgressed, commonly used statistics based on both haplotype as well as allele frequency information were employed to test for positive selection. Introgression by itself, however, changes both the haplotype structure and the distribution of allele frequencies, thus confounding traditional tests for detecting positive selection. Therefore, patterns generated by introgression alone may lead to false inferences of positive selection. Here we explore models involving both introgression and positive selection to investigate the behavior of various statistics under adaptive introgression. In particular, we find that the number and allelic frequencies of sites that are uniquely shared between archaic humans and specific present-day populations are particularly useful for detecting adaptive introgression. We then examine the 1000 Genomes dataset to identify regions that were likely subject to adaptive introgression and discuss some of the most promising candidate genes located in these regions.