Non-parametric linkage analysis examines similarities among affected relatives in alleles of one or more genetic markers (pieces of DNA at known locations on a chromosome). The objective is to evaluate departures from the null hypothesis that the markers are not near a disease gene. Under the null hypothesis, Mendel's laws give the probabilities that a set of relatives exhibits a particular allele-sharing pattern, and the null hypothesis is rejected if the extent of allele sharing among affected relatives exceeds Mendelian expectation. Because the rationale for allele-sharing methods is intuitively plausible and easily grasped, geneticists have used these methods for more than 30 years, well before the advent of the large sets of polymorphic markers that have made linkage analysis so fruitful today. Here we describe methods for assessing whether the extent of marker allele sharing among affected relatives exceeds Mendelian expectation. We first quantify the notion of allele sharing and the probabilities of allele sharing in various sets of relatives. Then we describe allele sharing methods for affected sibs and more general sets of relatives. We also discuss related issues of test size and power. We conclude with a brief discussion of areas in need of further research.