Recent progress in characterizing human genetic variation and its organization in several ethnically diverse groups coupled with advances in computational algorithms and computing power have yielded unprecedented opportunities to interrogate the human genome. It is now possible and commonplace to conduct genomic scans using large panels of markers to identify locations that likely harbor disease genes and to investigate interactions with other genetic or environmental factors. The primary analytic approaches for gene mapping, discovery, and statistical characterization of the genotype-phenotype relationship are linkage and association studies. Here, we review basic concepts, the biological and population genetic basis of linkage and linkage disequilibrium, and the common approaches used to assess these relationships with the goal of identifying loci influencing complex phenotypes of biomedical importance that could provide a rational basis for advancing genomic medicine. Further, we comment on the state of the science, recent successes, and the possible shortcomings of these approaches. Finally, we highlight some of the major challenges that arise from these investigative approaches and those that are inherent in the nature of complex traits. Many of these topics will be elaborated in the chapters that follow.