The availability and affordability of high density genotyping platforms have presented the genetics community with new opportunities as well as novel challenges for analysis. The existence of long stretches of homozygous markers is one of the features that have been noticed in recently acquired high density genotype datasets. These long stretches of homozygous markers are interesting as they can be signatures of copy number variations, inbreeding, depleted recombination, or selection. This thesis proposes statistical methodologies that aim at identifying and interpreting such homozygous segments. The introductory chapter 1 defines the problem and describes previous modeling efforts; chapter 2 proposes a model to detect genomic losses and map tumor suppressor genes on the basis of high density genotypes using tumor cell lines; chapter 3 discusses how to use such data to estimate inbreeding coefficient and extends the algorithm to account for linkage disequilibrium effects; and chapter 4 presents some further extensions of the model.