Some predict that influenza A H5N1 will be the cause of a 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 3 molecular evolutionary questions: (1) Have drug-resistant genotypes arisen in distinct lineages of H5N1 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 covariation 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 proliferate across the landscape by projecting or phylogenetic analysis onto a virtual globe. Our results for H5N1 show that in most cases drug resistance has arisen by independent point mutations rather than reassortment or covariation. Furthermore, we found that some codons that mediate resistance to adamantane derivatives are under positive selection, but did not find positive selection on codons that mediate resistance to oseltamivir. 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.