Diseases affecting hemoglobin synthesis and function are extremely common worldwide. More than 1000 naturally occurring human hemoglobin variants with single amino acid substitutions throughout the molecule have been discovered, mainly through their clinical and/or laboratory manifestations. These variants alter hemoglobin structure and biochemical properties with physiological effects ranging from insignificant to severe. Studies of these mutations in patients and in the laboratory have produced a wealth of information on hemoglobin biochemistry and biology with significant implications for hematology practice. More generally, landmark studies of hemoglobin performed over the past 60 years have established important paradigms for the disciplines of structural biology, genetics, biochemistry, and medicine. Here we review the major classes of hemoglobin variants, emphasizing general concepts and illustrative examples.