Genetic gain and rate of inbreeding are the 2 most important parameters to assess in livestock breeding. Genetic gain is defined as the increase in population-mean true breeding value over time. Rate of inbreeding has traditionally been estimated from pedigree information. The underlying assumption of this measure is that pedigree rate of inbreeding is a good proxy for inbreeding in the genome. While pedigree rate of inbreeding is the expected proportional loss of genetic variance at a neutral locus, it is not always a good proxy of loss of genetic variation at genomic regions harboring genes under selection. Therefore alternative measures of loss of genetic variation, or equivalently rate of inbreeding, have been proposed. The measures are developed for different information sources: SNP sets from chips or sequence data; and they use this information in different ways: assuming independence of SNP or specifically modeling the dependence between loci. The best of these depends on the purpose: is it for monitoring or is it for assisting decision making. The G-matrix was suggested by VanRaden in 2008 and has since been used with minor modifications in prediction of breeding values. While the different versions of the G-matrix appear to result in equally good predictions, the interpretation of its elements is not straightforward. Moreover, the use of a G-matrix instead of a relationship matrix based on pedigree information (A) in an optimum-contribution selection framework can result in less genetic gain at similar rates of inbreeding. The major short-coming of this method is that it does not use the information that the SNP included are mutually dependent due to the inheritance of segments of chromosomes carrying multiple loci. Therefore, theoretically, methods that use information on the linkage disequilibrium between SNP should give better results. One major issue that needs to be solved is what the gold standard is. For simulation purposes, we should be able to agree upon a best criterion, parallel to true breeding value in terms of evaluating genetic gain. Having agreed upon such a best criterion, the question remains, which estimator obtainable from real data is the best proxy for this best criterion.