A great number of physiological and anthropological studies have investigated Andean and Himalayan populations native to high altitude (HA). A non-scientific survey of the extant literature reveals a relatively liberal tradition of inferring genetic (evolutionary) adaptation to HA in these groups, often based on limited evidence and/or based on study designs insufficient to fully address the issue. Rather than review the evidence for or against genetic adaptation, and in order to provide some perspective, this paper will review relevant conceptual, methodological, and statistical issues that are germane to the study of HA native human groups. In particular, focus will be on the limitations of the most common research approach which bases evolutionary inference on the comparison of phenotypic mean differences between highland and lowland native populations. The migrant study approach is discussed, as is a relatively new approach based on genetic admixture in hybrid populations.