One century ago, Mendel's work was rediscovered, and in the subsequent twenty years the role of the chromosomes and genetic linkage in the inheritance of traits was well established. Within the next twenty, emerging principles of likelihood estimation and testing were applied to linkage inferences from data on human genetic traits. In the last twenty years, the revolution in molecular technology has allowed the detection and analysis of genetic variation at the DNA level. This has led to a wealth of data undreamed of by the early researchers, but the methods they established 50 years ago have been immensely successful in the mapping of of single-locus Mendelian traits.

Analyses of complex traits have, however, been limited by availability of and sampling strategies for trait data, by phenotype models and phenotype definition, and by computational power and statistical methods. Despite current enthusiasms for sampling designs that are variants of a case-control study, there is ultimately no substitute for the analysis of linkage---the cosegregation of genes. Markov chain Monte Carlo methods make possible the analysis of genome sharing among relatives, jointly over relatives and over loci. Such genome sharing analyses may be used in linkage detection, the determination of segregating pedigrees, and the identification of gene carriers.