A study of the inbreeding of UK Holstein cows was undertaken to assess the current levels and trends in inbreeding in this breed. Results showed that inbreeding has increased at a rate of 0.17% per year and it continues to increase in a linear fashion. Optimisation procedures, which have been developed to maximise the rate of genetic gain at a predefined rate of inbreeding, were applied to determine is such procedures would be useful in a dairy cattle context. The results showed that the procedures were able to generate more genetic gain at current rates of inbreeding or alternatively to reduce the rate of inbreeding at the current rate of genetic gain. Many resources have been devoted to the mapping of quantitative trait loci (QTL) of economic importance in most domestic livestock species. In the thesis a method is described to assess the benefits of using DNA tests at the commercial herd level. This method can be used for a variety of situations and two case studies were examined to illustrate the usefulness of the method. The first study dealt with the situation in which a breeder chooses to use a sire that is a carrier for a deleterious allele. The second case dealt with the availability of a DNA test for the A2 variant of the casein milk protein for which a premium is paid. Through a stochastic simulation, it is shown that pleiotropic QTL can result in a QTL segregating at constant frequencies in a population when the estimated polygenic correlation is zero.  This has important implications when, for example, the traits under consideration are production and disease-type traits. Various selection strategies were investigated to determine genetic gain and changes in allele frequency when the underlying genetic model for the QTL was different in both traits.