Some predict that influenza A/H5N1 will be the cause of a future pandemic among humans. In preparation for such an event, many governments and organizations have stockpiled antiviral drugs such as oseltamivir (Tamiflu®). However, it is known that multiple lineages of H5N1 are already resistant to another class of drugs, adamantane derivatives, and a few lineages are resistant to oseltamivir. What is less well understood is the evolutionary history of the mutations that confer drug resistance in the H5N1 population. In order to address this gap, we conducted phylogenetic analyses of 676 genomic sequences of H5N1 and used the resulting hypotheses as a basis for asking three molecular evolutionary questions: (1) Have drug-resistant H5N1 genotypes arisen in distinct lineages through point mutation or through reassortment? (2) Is there evidence for positive selection on the codons that lead to drug resistance? (3) Is there evidence for linkage between positions in the genome that confer resistance to drugs and other positions, unrelated to drug resistance that may be under selection for other phenotypes? We also examine how drug-resistant lineages are proliferating across the landscape by projecting a phylogenetic analysis onto a virtual globe. Our results show that in most cases, drug resistance in lineages of H5N1 has arisen by point mutations rather than reassortment. Furthermore, we found that some codons that mediate resistance to adamantane derivatives are under positive selection, but none that mediate resistance to oseltamivir are. We found evidence for one case of linkage via identification of covariation at a position that confers resistance to adamantane and another position on the genome. Together, our phylogenetic methods, molecular evolutionary analyses, and geographic visualization provide a framework for analysis of globally distributed genomic data that can be used to monitor the evolution of drug resistance.